Like all tools, spellcheckers are only as good as the humans who designed them and the human operating them.
What this means is: be careful with what your software's spellchecker recommends, and do not accept it blindly. The first word on a spellchecker's list of suggestions is not always the one you meant, and should a typo result in another correct word, the spellchecker cannot help you (for example you might have "statue" instead of "status".
The spellchecker category lists some common mistakes spellcheckers make. You may find your particular software has its own quirks.
Only careful proofreading can guarantee your work is free of mistakes.