What is this symbol in a financial record from Wisconsin, USA, in 1860?

Doubt it's anything special, other than the really common '/-' indication which even I use for cheques and other written entries. The '/-' indication is used to indicate the end of a number i.e. no further digits are to be added. Very common, and often recommended to do so in the not so digitized world, so as to prevent fraud (fraudsters can easily add more zeroes at the end to tamper with).

As to why the original author used them, force of habit perhaps? It's hard to glean whether the numbers are accurate, without much context. For one, we don't know what units they are referring to. Also, the data isn't normalized to a given time duration - one column has weeks, the other has a month, another has a number I assume is 75 cents, so must be on a per-hour basis....

Having tracked down the Instructions to U.S. Marshals, Instructions to Assistants for the 1860 census I draw attention to these excerpts describing the means of calculating and recording then census:

Schedule No. 1 - Free Inhabitants

• Item 12. Value of real Estate
  ..., and are to insert this amount in dollars, be the estate located where it may. ....

• Item 13. Value of Personal Estate
  Under heading 9, insert (in dollars) the value of all property or estate, ....

Schedule No. 4 - Agriculture;

• Item 4: Value of Farms
  

In this, as in all cases where an amount of money is stated, make your figures represent dollars; thus if the cash value of the farm be five thousand dollars, insert simply the figures 5,000. This rule must be particularly and carefully observed in all cases where amounts of money ate to be entered in the columns.

• Item 48. Animals Slaughtered

..., insert in dollars the value of all animals slaughtered during the year

Given the above, I find speculation that the values of inquiry describes an amount in shillings highly suspect. Notwithstanding that a shilling coin was in ubiquitous circulation and usage at the time, it seems clear that all records of the Census were to be recorded in the legal measures of account of the nation: Dollars and Percents thereof.

Not following instructions

As found by Pieter Geerkens, the instructions for the 1860 census repeatedly state that values should be written in dollars only. However, from context, we can quickly rule out $12 and $10 as plausible values for these columns, so the logical conclusion is that the clerk failed to obey that instruction for these values, and wrote the prices in terms that he was familiar with in every day life.

The symbol

I believe the symbol shown is the "solidus", a symbol for the shilling which evolved over time from a "long s" to an oblique or slash.

In the pre-decimal currency of pounds, shillings, and pence, used in the UK until 1972, it was common to write prices with shillings and pence divided with this mark, so that "2/6" meant "2 shillings and 6 pence". In this notation, two shillings exactly would be written "2/-". Written in cursive script, this would look exactly as shown in your image, with a tall oblique, and the "/-" joined up to the preceding number.

This would make the values "12 shillings" and "10 shillings", respectively. But whose "shilling", and what was it worth in US dollars?

The circulation of multiple currencies

In 1857 an Act was passed in the US Congress officially revoking the legal tender status of foreign coins, which up until then had been encouraged because not enough locally minted coins were available.

These weren't going to disappear overnight, so we can assume that in 1860 many people were still accustomed to them in every day life. This would also make sense of the reminders in the census instructions to write values in dollars - today, it would mostly go without saying, since the US Dollar is firmly established as the local currency.

The British shilling - a red herring

The most obvious shilling to look at is the British one - worth twelve pence, and one-twentieth of a pound sterling. According to this Encyclopedia Britannica article, the values of the two currencies on the gold standard valued 1 British pound at 4.8665 U.S. dollars (113.00 grains of gold vs 23.22 grains).

A shilling would thus be $4.8665 / 20, which is just over 24 cents. This leads to values of $2.92 and $2.43, which seem suspiciously high given the context provided.

American shillings

The Merriam-Webster entry for "shilling" includes this broad definition:

any of several early American coins

This confirms that the term was in colloquial use, and even in some cases the official name of coins with varying values.

The Spanish "shilling"

The currencies specifically mentioned in the 1857 Act are not British currency, but the Spanish and Mexican dollar. These were the basis of the US dollar, and were widely used at the time. Two noteworthy things can be seen in the Act:

• The Spanish dollar was generally being treated as equivalent in value to the US dollar. The Act makes provision to redeem coins for less than that value after two years have passed, because they wanted to take them out of circulation.
• The conventional fractions of this coin were not based on hundredths like the US Dollar, but halves, quarters, eighths, and sixteenths. (This is the origin of the term "pieces of eight" - a Spanish dollar divided into eight pieces.)

One eighth of a Spanish dollar was called a "real", plural "reales". These appear to have been in common usage at the time, and had various nicknames in different parts of the country (see for instance this article and this quote and discussion). These apparently included "bit", "levy" ... and "shilling".

The possible value

If taken as one-eighth of a US Dollar, a real would be worth 12.5 cents. (Since a British shilling was worth 12 pence, this multiple may explain the colloquial usage.)

If this is indeed the "shilling" meant by the clerk filling in this form, we would have values of $1.50 for "12/-" and $1.25 for "10/-", which are right in the middle of your ranges from other counties.

A caveat

This is definitely not a conclusive answer, and there are other possible interpretations along similar lines: "shilling", or just the shilling symbol, might have colloquially been used for 12 cents (in the same way "penny" colloquially means 1 cent), or a dime (a division between cents and dollars in the same way a shilling was between pence and pounds), or some other obsolete coin in local use.

That looks like the archaic form of the letter "s". Shown here in the word "Congress" from the original US Bill of Rights:

The Latin name for that long-s glyph is "solidus", which also happens to be the word from which we got the word "shilling". Of course this was not a coincidence. This glyph looks a bit like a slash '/', but is different (note that in the ledger it dips below the line, and curls outward a bit at the tips). Solidus was (and in some places still is) used as a currency separator, particularly between shillings and pence.

So looks very much like that indicates the units on the entry are in shillings. Of course the USA had been on the Dollar standard for quite a while by then, but it does appear that people in the USA were in fact still also occasionally using shillings as a unit into the 1860s, valued at 24 US cents each¹.

Supposedly, in old-fashioned £sd Accounting, a notation of "X/Y" meant "X shillings, Y pence". A dash in the pence slot ("X/-") meant 0 pence.

So those columns would be "12 shillings, 0 pence" and "10 shillings, 0 pence" respectively.

According to our Wikipedia reference ,that would be about $2.88 and $2.40 respectively. However, it was pointed out in comments that the 24 figure isn't very well documented¹, and the more typical factor in standard £sd accounting is 12. That would cut those figures in half, to $1.44 and $1.20 respectively, which is a figure more in line with what Semaphore reports as the average for those two columns in that state ($1.73 and $1.30).

^{1 - I tried to find a better reference for this, but it quickly looked to be an effort worthy of its own question.}