What major difficulties are faced while planning an international trip?

The biggest difficulties (IMO) according to what I see here...

1. Figuring out if you need a visa and which type of visa you need.
2. How can I use my phone while abroad (unlocking phone, sim card ... )
3. How to carry money (cash vs. debit vs. credit)
4. Do I need to learn the local language.

In my personal experience when traveling in Europe (from North America), the phone thing is the biggest pain (but it is mostly because I am too lazy figuring things out).

A trip is like a puzzle. The bigger and more complex the trip, the most difficult it is to plan. Recently, I came back from the most complex trip I have ever taken, an 80-day journey around the world with 15 international flights, 6 domestic ones, boats, trains, buses, etc.

• The biggest difficulty is making the pieces fit together. You need transport between multiple points and time in between to actual experience each destination. This inherently comes with risks as there can be delay and changes beyond your control, so you must carefully be conservative even if the routing tables say something is possible, it doesn't mean it will happen.
• The second part - which is only required for some trips - is obtaining visas. Every country seems to have a slightly different process and rules regarding this. The risky part here is that none will guarantee that you shall obtain the visa but in the process they may ask you for proof of lodging and onward travel. Hotels are commonly reserved in a way that the stay can be cancelled and you get reimbursed but fully refundable flights cost much more than non-refundable ones.
• The third biggest challenge is deciding what to take and how to pack it, while making sure to be within the official limits restricting carry-on luggage, personal items, checked luggage. Allowance can vary considerably, from a certain amount to half, as I recently experienced. You basically have to predict what you need during the trip and fit any valuables and essentials within what you can take with you on board. So if you have to take an international flight but then a domestic one and follow it with a boat trip, you have to make sure that whatever your bags are allowed by all three transports, in size and weight.
• Part of the above point is deciding what to use as luggage. A suitcase is a classic but there are many times when it becomes cumbersome. If you plan on hiking to go between places (not as a day trip where you can leave stuff and come back to them) then you should really use a heavy backpack, preferably with detachable carry-on/day-pack.
• Access to money can be an issue depending where you go. Travelers must research if their Bank or Credit cards are expected to work where they are going. This means being careful about the networks available (Cirrus, Plus, Maestro, etc) and if cards with chip are required. Somethings can only be paid by card, like completely automatic gas stations, while others require cash. It is always possible to acquire the local currency when arriving but that also means having one that will be accepted (usually USD and EUR are most popular). Calculating how much money that is to be taken out is also a challenge, depending on fee structure (with flat fee you should take as much as needed, with percentage you can split and reduce risk). Changing money back at the end of the trip nearly involves a loss, good estimation is critical.
• Transport and access to medicine can be a serious concern for those with certain health issues. They need to obtain sufficient medicine for the entire trip plus possible delay and they are rules governing how some can be transported such as refrigeration and use of needles for example. You might have to get refills abroad which means location suitable medical services and going through the language barrier to get them. Some medicines may be legal in one country but not in others which may cause problems.

There are certainly many many other things that must be handled with planning a trip but many of them are relatively easy with a few Google searches: Entry (visa) requirements, electricity voltage and plug type, weather, currency, language, vaccination requirements.

Honestly, while a phone is a nice safety item to have. If you have one that doesn't abroad, you can rent one or just the SIM if yours is unlocked and that is the issue, but even if you end up without a working phone. It is not much of an issue. Internet reaches far these days and you can make voice calls through Hangouts, Facebook and a number of over online services. Those who travel for business may be a little more concerned about this though.