I don't believe there's an exact word for "someone who corrects others' spelling errors", but there is one for a person who is meticulous in spelling, generally:
orthographer (lit. "right writer"): One versed in orthography; one who spells words correctly, according to approved usage.
If there is a single word which indicates (as @ermanen puts it) a "spelling Nazi", it will almost certainly be derived from "orthography" or "orthographer"; you might consider deriving one yourself, or popularizing a new sense for an existing word, such as:
"orthographizer", derived from "orthographize" meaning "to write or spell correctly", which (I think) nicely emphasizes the transitive nature of his compulsion (i.e. not only ensuring his spelling is perfect, but yours, too), or
"orthographist", has the advantage of possessing that dogmatic little tail, -ism, but is currently only used to describe a specialist in orthography, or "one who studies orthography". So you can either popularize a new sense for it, or extend it a bit to underscore the adherence to received protocols (an "orthodoxic orthographist"? an "observant othographer"? the possibilities are endless).
EDIT: You might also consider unpopular :)