When I drive to the local park and fly my P3P all is good.  However, when I fly at home in my neighborhood I always have signal problems ranging from compass error to lost GPS.
Is it possible that the wireless routers in my neighborhood has an effect on the drone and controller connection?

Definitely!  More like signal loss between controller and drone.  Compass and GPS loss would be odd though unless large metal structures are nearby, or buildings/trees blocking satellites.

That's very likely to be the case. A lot of home WiFi's run on 2.4 GHz and can muddly up the RC connection. Depending on whether or not you're in a more urban environment, you're most likely running into metal and electrical interference.

I crashed my drone a while back, sent it in for repair, and ever since I get the same type of signal problems in my neighborhood. However, every thing change when I installed the cheapo range extenders.