I had a problem with my Apple Watch recording too many exercise minutes:
I went down the full troubleshooting tree with the Apple Support rep: turning Fitness Tracking under the Motion & Fitness Privacy Settings off and on again; resetting the calibration data, turning the Watch off and on again, and un-pairing and re-pairing the Watch.
It seemed to work a couple of times, but a day or two later the Watch would go crazy again, recording hundreds of minutes of Exercise just by sitting still. I even sent the Watch in for repair, but it came back with nothing showing up on the diagnostics.
It turns out the problem was with my weight. The Watch seems to use weight in its exercise calculation. I had set my weight when I set up the Watch, but I also used a workflow in the Workflow app to update my weight for the Health app every morning. The problem was that the workflow was writing bad data to the Health app (0.05 kg, for example). When the Watch thinks you only weigh 0.05 kg, then you get a lot of exercise by just sitting still.
If you're having problems with way too many exercise minutes, open the Health app and look for Health Data... Body Measurements... Weight to make sure the Watch doesn't have bad data that it is using to mis-calculate your exercise.
I hope this helps someone else!