How Do You Tell The Difference Between Scott 179 And 181?

The catalogue says the Scott 179 is on yellowish wove paper and the 181 is on Hard white wove paper without gum. The paper on this stamp looks very white, any possibility it is a Scott 181?

Not very probable that its Sc 181, the Special Printing. Very few of that special printing were sold to the public as the stamps were then in circulation. The special printing was for the Centennial Exposition of 1876. Continental BN Co. had just begun printing Sc 179 in June of 1875. All of that said, there is a slim chance that it is 181, you'd need to get it certified to be sure, have never read of one used, but that doesn't mean someone didn't use one.
Notice where I drew a box around what looks like a possible double transfer.

The departmental stamps (officials) on hard paper overprinted SPECIMEN are special printings produced at the same time as the other reprints. reissues, and special printings in 1875. Get yourself an example of one of those and you will have a sample of the hard, white, paper of the special printings to compare. When they look REALLY close, then send in your suspected copy. However, note this, except for the 3c and 24c values the Bank Note Special Printings are not listed used because they are not known used. You will have a steep uphill battle trying to get a used stamp certified.

I should also have mentioned a caveat: some of the departmental special printings were done on a particular kind of horizontally ribbed paper. I have one for the 1c Justice dept. Don't use those as touchstone examples. The US Specialized will give you a complete roster of issues known on this paper.

I thought the area you highlighted was just a kiss print. Here is a closer view.

Maybe just old ink?

It's not a 181, the impression isn't right for one. Plus, 10 181s exist, 9 of which are privately held.

I knew that there were not many sold to the public, but 10! Yeah, pretty sure it's not Sc 181! What essayk said about the departmental specimen stamps is true for the first printing of the specimens, but the 1 cent Agriculture, Executive, Navy, and State specimens had a second printing and those are on ribbed paper. There are also three other printings. The American BN Co printed 5000 each of the 1 cent Executive and the 1 cent Navy, they are on soft paper. The 4th printing consists of one stamp, the 1 cent State, also by the American BN CO, on a soft thinner and silker paper than the typical American paper. The 5th printing by American BN Co consisted of 5000 each of the 1c Agriculture and the 1c Executive, but the quanities on hand proved to be enough to meet the demand and these were destroyed.

billw2, could you please go into some detail about your comment on the impression--would be a good learning experience I believe. Scans/photos would be appreciated too if available.

Let's not confuse the issue with too much data. The original question was about paper for a special printing. My recommendation to use a hard paper Departmental specimen overprint as a touchstone for the paper still stands. I was careful to point out the existence of ribbed paper as something to set aside, and littleriverphil has kindly referenced that for the second printing. So it comes down to the printing on hard paper, and those stamps are readily available.

billw2 has mentioned the problems with impression if one is looking at this as a Special Printing, and I concur with that 100%. Look at the poor quality of the lines in the closeup above, particularly the vertical shading lines in the background shield, and you can see the problem. The SP sheets were done as low production on special paper for a proof-like quality. The don't look like this one.

So what is your opinion on the splotched lettering on the upper right corner?

I think this looks like a rusted plate flaw.

DBL transfer or plate flaw, opinions please.