There is an updated version of this post here.
Paradoxically, a spell-checker is only useful if you can spell! It's a common misunderstanding that if you can't spell, a spell-checker will sort things out for you. It won't.
There are four things a spell-checker simply cannot do for you:
It cannot decide what word you want to use. For example, if you have typed the word "theer", it will suggest three and there: you will have to decide which (if any) it should be.
It cannot recognise proper names (especially surnames). For example, if you type a letter to me addressed to "Mr Fredman", it won't know that you mean to write "Freedman".
It cannot distinguish between homonyms, ie words that sound the same but don't mean the same. For example, it does not know the difference between "you" and "ewe".
It cannot know that you are using the wrong word entirely. For example, it will not know the difference between "continual" and "continuous".
In other words, spell-checkers are useful, but not intelligent. You should not rely on it if you are trying to impress an editor! Sad to say, you cannot escape from the task of proof-reading.
When proof-reading, you should consider doing the following:
Ask someone else to proof-read it. The mind had a habit of making you see what you know should be there rather than what is there. That's why, for example, it's very hard to spot missing words: the mind puts them in.
Make sure you are using words correctly. A dictionary may not be enough: invest in a dictionary of usage and abusive as well.
When using your spell-checker, use the Add facility to add words like your surname, or specialist jargon, to the dictionary, so that those words are not flagged up as mistakes in future. But be careful: it's all too easy to accidentally hit the Add key and cause a mis-spelt word to be inserted into the dictionary, meaning that in future that particular mistake will never be picked up!