Thank for the help, everyone. The model # is 3222C-Z, and here's a link to the manual:
http://www.wayne-dalton.com/Files/P...or_Openers/prodrive/325809 Rev5 7-16-2008.pdf
I looked through the manual but only saw that if I hold down the program button for 10 secs the opener will completely reset. I'll try that.
A common builder did build the homes in our neighborhood. I'm not sure what, if anything, our neighbor has done differently over the past week. I haven't met them yet, but I may go talk to them this weekend.
Our remote does not activate their door.
What's really odd is last night the door opened without anyone noticeably nearby. The other times it has opened I've been able to look out the window and see that our door is opening/closing in sync with our neighbor's door (they live across the street to the right).
One thing that did happen recently is the remote wireless outdoor entry pad malfunctioned due to rainwater getting in the unit. I took it off and tried to dry it, but it still wouldn't work. I removed it completely today, and I don't know how that might affect this issue (if at all), but we'll see.