This morning I had to change my rear tire and tube, and during my subsequent ride my rear derailleur constantly slipped out of gear and skipped gears. It has never been a problem before. How do I fix it? I'm riding a mountain bike with a Shimano Alivio derailleur. Thanks.

Make sure your wheel is properly seated in the drop outs. I'd be surprised if you messed up the derailleur, shifter or cable tension just by removing a wheel. My guess is that it is not properly seated.

hopefully you did not bend the rear derailleur hanger. I work as a bicycle tech and I see this problem over and over again. You'll need specialized tools to fix this problem if your rear derailleur hanger got bent.

This would be my guess too. The bike needs to be in a wheels down position when the quick release or lock nuts are tightened on the dropouts. Axle needs to be fully seated.
A bent derailleur hanger is also a possibility. A bike should be on the non-drive side when on the ground.