Have there been any nuclear accidents in the US at nuclear facilities which were not "commercial"?

The New York Times article is undoubtedly referring to the deaths of Harry Daghlian and Louis Slotin. Since noone died in the Three Mile Island accident, the Daghlian and Slotin deaths could be considered worse accidents. There were also 2 deaths and a critical injury due to a non-nuclear chemical exposure at the Philadelphia Navy Yard in 1944 as part of the Manhatten Project.

Since the war, there has been various deaths at government labs and military facilities. Cecil Kelley was killed in 1958 at Los Alamos after a massive radiation exposure. In 1961, an experimental reactor in Idaho called SL-1 had a meltdown and killed the three men present at the time.

The Demon Core was a 6kg sphere of Plutonium that was involved in two criticality incidents in the forties at Los Alamos, each time resulting in the death of the scientist involved in the experiment.

Just about all the serious accidents and deaths have occurred in US military facilities (land or sea based). Ditto in the old Soviet Union.

This is because of the military cultural tendency to play fast and loose with safety protocols (and the same reason is why ex-military pilots don't make good airline pilots - they'll push on when other pilots will turn around and go someplace safer)

Three Mile Island was a case of "Oops, shut it down and we'll clean it up when the radiation levels are low enough to go in" (this is happening now). The safety systems all worked as they were supposed to, despite some major furrfus in the design - there was so much redundancy in the systems that once it was realised what was going on, things were brought under control fairly quickly.

Chernobyl was amazingly bad (the operators deliberately switched off all the safety systems to run a test of how far they could push it before it broke and lost that bet) but overall it didn't release all that much radiation into the atmosphere (the world's coal fleets release about as much as radium each year) compared to the 1950s atmospheric nuke tests and all the deaths were caused by acute exposure to the fiercely gamma-emitting burning reactor core in the first week There will be more deaths, but a couple of hundred at most. Acute radiation exposure tends to either kill people relatively quickly or not kill them at all and airline crew get hundreds of times more exposure than any nuclear workers each year, which is a good indication that chronic exposure needs to be fairly high to matter (The cancer rate in Hiroshima and Nagasaki was down to 0.25% above background levels by the 1980s and 2nd generational effects turned out to be virtually non-existant despite fears at the time)

The UK's Sellafield/Windscale accident was at a mixed-use site but the reactor in question was strictly for bomb-making, not civil use (it's still too hot to approach)

Chernobyl is (so far) the only civilian plant with large numbers of deaths from an accident. There have been a few freak incidents where careless workers managed to kill themselves via gamma ray exposure (The most peculiar was a reprocessing plant in Japan where the workers managed to do it whilst mixing chemicals in a plastic drum of mostly water) but statistically nuclear power is the safest form of energy per TW generated - and by several orders of magnitude. Skip to 2:38 on https://www.youtube.com/watch?v=4E2GTg7W7Rc to see the comparison.

More people were injured in the panic trying to get away from TMI than by the actual steam leak (which was fairly benign) and over at Fukushima, whilst 20,000+ people died in the Tsunami, the death toll at the nuclear plant was 1 Crane operator whose machine toppled in the quake, and a few techs with very light (easily treatable) radiation burns on their calves as a result of standing in radioactive water for several hours.

The big environmental messes which are (still) being cleaned up are almost entirely military in origin - see comment above about playing fast and loose with safety.

That said, boiling/pressurised water reactor systems are intrinsically unsafe just like any other high pressure boiler system (high pressure, high temperature water is extremely corrosive and eventually will wreck the boiler) and when circulated in a nuclear core, water ends up picking up radioactive contaminants, which is a bad thing if it ends up leaking (water's sometimes jokingly known as "the Universal Solvent").

Just about all the incidents in working civil plants have been down to issues revolving around corrosion and management cutting corners on maintenance or safety circuits. That happens in coal plants too, but coal plant boiler blowouts aren't headline news outside the local area.

There are arguably better designs for civil use but the Cold War resulted in a 40-year fixation on designs which could produce plutonium with civil use as a sideline, vs designs which are really good at producing heat for civiluse but pretty much useless for producing bomb-making materials. Expect to see those "better" designs start to hit the marketplace in the next decade or less - around 50 years since the first (and last) of their type was switched off for the last time in 1969.

Hopefully "atoms for peace" will finally happen, because there simply isn't enough space to put all the windmills and solar panels needed to satisfy current electricity demands, let alone the ramping up that will occur as gas and oil home heating systems die off and we move inexorably towards more-electric vehicles.

Hanford, right on the Columbia River which flows through my city of Portland, OR, is probably the largest non-commercial nuclear disaster in terms of cost and scale of environmental damage. Its a former top-secret nuclear processing facility for the US military.

Hanford was used for decades for nuclear processing with nine reactors and five plutonium processing plants to make the plutonium for most of the US nuclear arsenal. Their waste disposal procedures were dreadful, and because it was all top-secret they didn't have to deal with pesky regulators and inspections. Hanford left behind 53 million gallons of high level liquid nuclear waste, 25 million cubic feet of solid radioactive waste, and has contaminated the ground water for 200 square miles around. That's fully 2/3 of all the high level nuclear waste in the US. The storage tanks were leaking hundreds of gallons of waste for years. Hanford would use water from the Columbia to cool its reactors and pump it back into the river releasing long lived isotopes detectable 200 miles down river.

The cleanup has been going on for 25 years. They keep finding more undocumented contaminated hazardous material. It's been a trail of mismanagement. It's estimated cleanup will cost an additional $100 billion over 30 years involving 10,000 workers on site.

Beyond that, depends on what you call an accident. How about losing a nuclear bomb? How about losing several of them? These are known as Broken Arrow incidents and for the number there have been its surprising that none of them resulted in a nuclear explosion. Bomb designers know their job.

Here's a few sources to read with growing horror.

• Wikipedia's list of military nuclear accidents
• 5 times we almost nuked ourselves by accident
• US Nuclear Accidents
• Department Of Defense's Narrative Summaries Of Nuclear Accidents Involving U.S. Nuclear Weapons 1950-1980

Hard to say, military-related nuclear incidents tend to be classified.

But I'll wager a guess as to why New York Times felt the need to specify TMI was the worst commercial nuclear incident:

Commercial nuclear facility operators generaly operate under the supervision of International Atomic Energy Agency. Among other things, this agency defines an International Nuclear Event Scale, which is an easy way for the newsies to rank nuclear events from least serious to most serious.

Militaries sometimes have their own scales and terminologies, but these tend not to be clearly ranked and generally are more concerned with things such as misplaced, malfunctioning or accidentally detonated nuclear warheads.

It's going to depend on how you define "nuclear accident" and how you define "worst."

USS Thresher (SSN-593) went down with all hands in 1963. The cause (we think) was a significant sea-water leak (flooding casualty). The reactor was scrammed (emergency shut down), and without its main source of propulsion the submarine sank. Everyone on-board was killed. Certainly bad - over 100 people killed and a multimillion dollar warship lost, but is it a "nuclear accident?"

Or:

In 1961 a US Army reactor (SL-1) exploded, killing three people. This occurred in a remote area in Idaho, so exposure to the public was negligible, and it was (relative to other nuclear incidents) in-expensive to clean up. This is certainly a nuclear accident, but is it "worse" than TMI, which received national attention, caused fear of widespread contamination, and was very expensive to stabilize? People die in industrial accidents all the time.

At the end of the day, TMI released very little contamination to the environment, and what it did release was short lived (generally hours to days range), and there were no fatalities. From a public health stand-point it was a non-event. From a public perception stand-point it was a disaster. From a financial standpoint, it was a disaster.

Whether events like the Thresher or SL-1 are "worse nuclear disasters" is something that could be debated, and I'm sure family members of Thresher sailors or SL-1 soldiers would be angry if they felt their loved ones were being minimized in some way. By restricting it's assessment to civilian accidents the NYT avoids potential controversy. To my knowledge, no other US civilian reactor has experienced core damage anywhere near as severe as TMI, and certainly none have received anything approaching the public attention.

Yes. SL-1 is estimated to have resulted in a release of about four to five times as much I-131.
SL-1 may have been made public because the scale and location of the event made it difficult to hide. It may also not have been considered sufficiently sensitive to warrant extreme secrecy, unlike projects such as aircraft nuclear propulsion.

I suppose you could consider Castle Bravo to be a 'nuclear accident.' While we did intend to nuke the atoll, we didn't intend the blast to be anywhere nearly as large as it was, contaminate islands more than 100 miles away, or irradiate a Japanese fishing boat.

If you count Castle Bravo, it's almost certainly the largest in U.S. history, much worse than Three Mile. It's also the largest nuclear blast of any sort (intentional or otherwise) in U.S. history, even though it was the very first deliverable fusion device we tested. At that point we basically decided, "This is too big, let's build smaller ones from now on." The Russians made a similar decision after Tsar Bomba.

As far as the title question of whether there have been any accidents in U.S. non-commercial nuclear facilities, the answer is quite certainly, "Yes, lots." There was a single Plutonium core (nicknamed the "Demon Core") that was, by itself, involved in two accidents, both fatal. Later, it was successfully used in Crossroads Able at Bikini Atoll.

Wikipedia also has a List of military nuclear accidents. It's long. Perhaps one of the most amusing (which fortunately wasn't fatal,) was when the Air Force accidentally dropped a nuclear bomb on South Carolina. Thankfully, the nuclear core was not installed in the bomb (otherwise the results would not have been funny at all,) but the conventional high explosives that are used to start the first fission stage were in the bomb and detonated, leaving a 75-foot-wide crater in a farm.

It depends on what you consider worse.

Time magazine lists an incident that occurred on December 18 1970 at Yucca Flat Nuclear Test site where radioactive debris from the underground test of a 10 Kiloton Nuclear detonation was vented into the surrounding atmosphere. However the Department of Energy stated afterwards that the 86 workers who were exposed did not receive a dose that exceeded site guidelines (whatever they were...) (Source)

The USAF has had many nuclear related incidents, including recently (some are listed in the Time article above) which occurred outside of a Nuclear Facility (unless you count the aircraft carrying them as a Nuclear Facility).

For example, in 2007 a USAF B52 sat on the ground at Barksdale AFB for ~36 hours with six AGM-129 ACM Cruise Missiles, each containing a Nuclear warhead, without guard or any of the mandatory security measures in place because the warheads were supposed to be removed before flight. This is an example of a failure of procedure in a USAF base that could be argued as being a Nuclear facility, as the warheads should have been removed and logged into storage in an appropriate facility.

Furthermore, a recent Guardian (UK) article relates that in 1961 a 4 Megaton H-Bomb came perilously close to detonating after it was released when the bomber carrying it entered a tailspin. For one of the bombs 3 out of 4 safety mechanisms to prevent accidental detonation had failed to operate and that the forth (which saved the day) was highly vulnerable to failure.

The information in the article was uncovered by Eric Schlosser who, as covered in the article:

discovered that at least 700 "significant" accidents and incidents involving 1,250 nuclear weapons were recorded between 1950 and 1968 alone.

All of this comes with the caveat that I'm not at all qualified to describe any of these as being worse than Three Mile Island. Some are certainly much more terrifying to me personally.