What is wrong with "Where should this car be parked?"?

When used as a stand-alone sentence, you're right:

1) Where should this car be parked? <-- correct

2) Where this car should be parked?

Now... if it's part of a larger sentence it's different:

1) Do you know where should this car be parked?

2) Do you know where this car should be parked? <-- correct

I would speculate that either there was some other typo that made MS Word think you were in the second scenario, or it was just a flat-out bug in the grammar checker.

1. is right; 2. is wrong. The grammar checker probably got confused by the fact that if the question mark were omitted, it would be the other way round.

It may be possible to devise a computerised grammar for English that makes fewer mistakes than a schoolchild (always a good discussion topic in the bar), but Microsoft Word doesn't have one.