The thing with Word's grammer check and spell check features is that two people might get two different things if they have the settings changed.
For example, I have my grammer check set on formal writing, which catches way more than the default setting. Grammer check is really only useful for people who have a good grasp on grammer in the first place, because Word does not read what you write. It takes what it "sees" and suggests ways the writing might be better. Most of the time it is wrong. I use the formal setting mainly because it tells me where I have used passive voice.
Anyway, when it comes to spell check, Word is seriously lacking. If Word tells you that you are wrong in the way you have spelled something and you think you are right, look it up in a dictionary before you believe the program. Sometimes it needs you to tell it that grey and gray are both correct.
Also, if words like center/centre or tire/tyre are being corrected incorrectly for your language, make sure that the language your program is set to is the correct one. These spellings are American English/England's English respectively.