Sorry it took me so long to get back. Thanks for all the fun answers!
Water saving windows! -- LOL -- Yeah, that was just clumsy writing.
OK, the real clues burried in the description were:
Old house
Water saving appliances
New exterior doors (infer: old interior doors)
Fresh paint
It's not really fair because any of you who would have checked to see if the doors were square or if the latches were alligned with the strike plate would have probably noticed the real cause ...
All the interior doors and cupboards are original to the house and have been painted repeatedly over the past 57 years. The paint layers have built up to such a point that the paint on the hinge side of the door and door frame is so thick it puts pressure on the door to open. The latches have also gotten a little loose over the years and some of them don't extend all the way because paint on the edge of the mortise has restricted them. They still latch, but just barely. The doors will close and latch, but eventually they give in to the pressure from the paint build up and pop open.
The shower also wasn't fair because you would have had to look at it to figure it out. They installed a rain style shower head to compensate for low water pressure. (again I can't post a link to exactly what it looks like, but google "rain shower head" and you will see some examples).
The shower head holds about three cups of water. When you take a shower the water starts to drain back down the pipes and that suction prevents the water in the shower head from draining out into the shower. Eventually the suction breaks and all the water in the shower head comes cascading down as if the shower had been turned on full blast for a few seconds.
The thing about both of these "phenomena" is that they don't happen at predictable intervals after the actual cause -- the doors don't pop open right after you close them and the shower doesn't drain right after you get out of the shower, it can be anything from ten minutes to hours later.
Chaos I suppose. Anyway, the random time intervals between cause and effect make it possible to start inventing other possible causes.