Not trying to be a smartass but you should have done something about it when ypou first got the machine. The "wobbly teeth" were most likely caused by a previous owner letting the teeth wear through to the adapters at some point. The loose teeth is again most likely to be the root cause of your broken adapter. Tooth breakage is also down to adapters. Can you post some photos of what the adapters that are left on the bucket look like but with the teeth pulled off, especially from side on if you can manage it. Adapters can be welded up to bring them back to profile so the teeth are as tight as they should be (a bit of "wiggle" is normal) but depending on the condition of the rest of the adapter you might be better replacing them completely. Obviously the broken one has to be replaced, but I'm thinking about the others ....
Anyone having problems with the pin/retainer system on a Cat bucket should look at the adapter profile carefully and check for wear. Let me see if I can post some photos.......
OK, so here we have a classic case of an adapter where the tooth was not replaced soon enough. See the profile..? Compare that with the photo of what it's
supposed to look like. Lastly is a photo of the badly worn one from the 1st photo after being rebuilt.