I did not purchase the lens when buying the camera. I owned a M6 a few years ago and kept the C-Sonnar 50mm. It's currently my only M mount lens so I wasn't able to try any real Leica lenses. Guangong you make a great point. I didn't clean nor polish the mount. I just expected the lens to fit with no problems like it did on my previous M.
I sent the camera to KEH after my original post and they replaced the lens mount and back spring before sending it back. The lens now fits into place better than it did before. It's still a little rougher than it probably should be, but I'm glad to get it back.
My M2 (KEH Bgn) is an early model with the rewind button. Unfortunately the button and screw fell off the camera, and the collar that surrounds the button is really loose. I tried screwing it back on, but both the button and collar are still to loose, and fragile. They feel like they could fall off at anytime. I'm pretty disappointed, but decided to send it to DAG.