No, spell check does not catch every spelling error. For example, look at the followingsentence:
I want to sale the deep, blue sea.
The word thatisused incorrectly issale. Although this is a correct spelling of the word, it is not the spelling that fits in the sentence. Spell check did not flag this error (by putting a line under it, indicating an incorrect spelling).
Therefore, in addition to using the spell checker on your computer, it is imperative that you also read through each sentence along with having someone proofread the work.
For help with proofreading and more, visit the Writing Lab.