Spell check everything, but don't rely entirely spelling check. It can be a useful tool, but it's not. Spell check has a limited dictionary and some words will show as misspelled when they aren't. In addition, spell check will not catch misspellings that form another valid word. For example, if you type "your" instead of "you're" or "to" instead of "too", spell check won't catch the error.
Grammar check can be a nightmare. It will show the rule, but not apply it correctly. It also won't identify every grammar error. However, grammar check can be a tool for catching something you should think about; just don't automatically do what it tells you to do.
