My husband uses a mobility scooter and wonders if he would be able to go into any of the cliff dwellings
Welcome to the forums. I was in Mesa Verde last week and did a lot of the archaeological sites and the museum.
The archaeological sites are easy to see with paved/fine gravel walkways and limited handicapped parking. The challenge will be unloading and loading the scooter at each stop. If you go during the busy season it could be quite a challenge to manuever, imho, since it was crowded at some points with family groups. The museum and visitor center are both very scooter friendly and there is a great film at the museum. Be sure to bring binoculars and you can see Cliff Palace from a couple of different vantage points.
Only you can decide your strength in dealing with the scooter. Just doing the walking at altitude tired me out more than the usual stroll in the park so I think you should be acclimated before going up there. Hope this works out for you.