How to cite a paper with a typographical error in the title. In the reference list, should I correct it (and make it hard to find) or let it as is (and make an impression I was sloppy)?
This would be an excellent time to use the Latin sic:
("thus"; in full: sic erat scriptum, "thus was it written") inserted after a quoted word or passage, indicates that the quoted matter has been transcribed exactly as found in the source text, complete with any erroneous or archaic spelling, surprising assertion, faulty reasoning, or other matter that might otherwise be taken as an error of transcription. source
It is commonly used as a suffix in bracketed form after a citation e.g.
Charmley, John (2006). “The Princess and the Politicians” [sic]
or used after an erroneous word or passage
She wrote, “They made there [sic] beds.”
Do not correct it.
The purpose of references is to help readers locate your sources as easily as possible. Correcting titles might give the impression that you are referring to another work.
Do not correct it, if its only in the reference list then that's completely fine. If you actually refer to the name of the paper in yours, you may add "(Sic)" afterwards. (See https://en.wikipedia.org/wiki/Sic )
My personal solution to this is using square brackets, as often used for editorial adjustments. (In the sense of Brown: "This is a great idea." → Brown claims that "[t]his is a great idea.")
Similarly, you can cite
White, J. "A solution to the thee-body problem"
White, J. "A solution to the th[r]ee-body problem"
I think it's obvious enough that the [r] was inserted to improve an error and not the other way around. Also, if it were a play on words between "thee" and "three", it would be much more likely that round brackets were used, as in "th(r)ee". Outside formulae I would understand square brackets to be used for said "editorial adjustments" almost exclusively.
This best works when there is an extra or missing letter, but then all the typos I've come across in titles were of this type. For more serious errors, I would use [sic] or (sic). Also adding doi to a citation and paying attention to the issue numbers (which are sometimes not even printed on the published version) can help track down a paper with a misspelled title.