Love them or hate them, they are helpful and useful tools. In fact, I recommend every writer have Spell Check turned on at all times. In MSWord, that little red line will help you catch misspellings immediately. Then there's the blue line to alert you to the wrong spelling, or possibly the wrong word—also a useful tool. The green grammar lines? Those I tend to ignore since fiction writing takes some liberties with proper English.
Yeah, you knew that was coming. However. These built-in tools in super-smart word processing programs do not take the place of the human eye and, I hope, human intelligence.
Read the work out loud. Read it backwards. Read it very slowly, out loud, and backwards. Know your weaknesses and do searches for them. Surround yourself with excellent critique partners who will actually give you the bad news that your grammar stinks. Better them than a reader or reviewer. Find a beta reader who excelled in English. (Mine beat me bloody about improper and over-usage of the word “that.” Still does to this very day. And no, you may not have her name or email address. She’s all MINE.)