Check whether "it's" is used in a latex file. I consider "it's" to be bad form and prefer "it is". Also often shows up as a typo, when I actually meant "its".
Flycheck configuration is as follows:
(flycheck-define-checker latex-itis
"A LaTeX syntax checker that warns about the uses of it's."
:command ("itis" source)
:error-patterns
((error line-start (file-name) ":" line ":" column ": " (message) line-end))
:modes latex-mode
:error-filter
flycheck-increment-error-columns
:next-checkers (tex-chktex)
)
(add-to-list 'flycheck-checkers 'latex-itis)