The only time the doors on my 96 Avalon don't fully latch is when I just lightly push the door closed. However, if I close with normal strength, it has no problem latching fullway.
What's really an annoyance, however, is that the door is a bitch to close if latched halfway. You just can't "bump" it shut, you have to reopen and close again. I've never had this problem with my old gen 2 Camry or my truck, a simple push securely closed the doors on both vehicles. I guess it might have something to do with thicker door seals as this is a luxury car.
As far as the dome light remaining on, I am quite anal about double checking to see if all my electrical items are off before/after exiting the car (as well as making sure the windows/moonroof are closed before leaving the car). It's because this behavior why I've never had a dead battery (that, and the auto-off headlights

).
Also, if you have a Toyota security system, the door will not lock and the alarm will not arm if the door is left ajar.
--AvMan96