How fix two interior lighting problems?

I just bought this used Honda with 144,000 miles and have two minor
electrical problems, which I tried to fix with new bulbs. One is the passenger
map light. I replaced it. It worked, but then it started working when it should
be off. I think it burned out the bulb afterwards so now doesn't work again.
The other is the overhead dome light. I tried to replace the bulb but was
having difficulty getting the cover off. Then the light started working again,
like maybe the pressure had shifted something inside, but it also quit working  
again later on.  I'm thinking this is more than a fuse problem, and wonder if it
is likely to be expensive to fix?  Thanks for your advice....