Spell checkers are as accurate as the dictionaries they use, and they're more likely to mark properly spelled but uncommon words as misspellings instead of missing misspelled words. However, many can miss misspelled words starting with capital letters.
Because there are so many proper nouns, many spell checkers ignore words that start with capital letters, which can lead spell checks to miss misspelled words at the beginning of sentences. This also applies to acronyms. Dictionaries and style guides have different rules for spelling, so writers might be led astray by using a spell checker with spellings not used in the relevant style guide.