A nitpicker is a person who finds faults, however small or unimportant, everywhere they look. After seeing a movie, a nitpicker lists every tiny thing he or she didn't like about it.
Use the informal nitpicker when you're talking about someone who is extremely critical, even when those criticisms seem inconsequential. If you can always find something to complain about, you're probably a nitpicker. This word, from about 1950, comes from the idea of literally picking nits (or lice eggs) out of someone's hair — a nitpicker is as careful and meticulous about finding faults as a literal nitpicker would be about finding each tiny nit.