Dental bridge loose over root canal tooth that has lost structure and there is infection in gum. My dentist not concerned. Should I be?

Yes. Loose bridge indicates failure of cement seal or loss of bone support. Tooth "loosing structure" may mean ongoing decay. If your Dentist is unconcerned I would want a second opinion.
Dental infection. I would be more concerned about an infection than about a loose bridge. If you are in doubt, get another opinion from a dentist with exam and xray.