2001 325i Electrical problems?

Hi, Ive had this car for 3 years now and everything is GREAT, but suddenly this winter my passenger rear light turns off and on (lack of ground?) and then the front drivers side turn signal does the same
thing, the bulb doesnt burn out just burns near the plug and I can clean off and it works fine, any ideas?
Also this is the sports package model so it has white lights (sorry for better lack of terminalogy) and they started to flicker when it got real cold here in texas (30's F) are the bulbs dieing out or some kind of ciruitary issues? any opinions are appreciated, thanks...

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