Homonyms. Spell checkers cannot distinguish between words such as affect and effect that sound alike but are spelled differently.
Proper nouns. A spell checker cannot tell you when you have misspelled a proper name. Proofread names with special care.
Compound words written as two words. Spell checkers will not see a problem if nowhere is incorrectly written as no where. When in doubt, check a dictionary.
Typos. The spell checker will not flag heat even if you meant to type heart.