The battery door is replacable, as mentioned above. However, it is not replacable by the user. You need to remove the top of the camera, and it is complicated and difficult. You need to take it in and have the door replaced by an actual person or shop that does that kind of thing.
I read one web write-up describing how one guy forced the pin with needle nose pliars without removing the top, but I have been unable to get my pin to budge even with excessive force. I dare not risk the camera.
Best thing for the battery door is the "action grip" that screws over top of it. That will keep the sucker in place even after you break it, most times. What it doesn't keep in place a bit of electrical tape will do.
I have an AE-1P. It was my first SLR, and I still use it today. It is amazing in its simplicity and ease-of-use but will still allow you to do almost anything you want.
P.S. If you want shutter priority, set the shutter to program and manually select your f-stop. It will adjust accordingly. If you want aperture priority, set manual shutter speed and set f-stop to A or "dot". It will adjust accordingly. If you want it to think for you, set to program and A or "dot." Or it's nearly perfectly suited for full manual as well. The only thing I missed (and only on occassion) was an f-stop readout in the light meter LEDs. It wasn't necessary, though, and the shutter dial was so perfectly placed I could notch it up or down on the fly without even thinking for a fast light meter adjustment.
Awesome camera. Will last you 20 years if you CLA it once in a while.