I just noticed the same problems with my 1.1.1 phone yesterday, well not a lot as descriced but it happened when I played music and surfing on Safari @ the same time it just really frustrated to the point that I felt like upgrading it to 1.1.1 was a wrong decision ( used to work fine w 1.0.2), so I just left it full charged then turned it off completely for last night, it works fine today after half an hour checking in the morning, but I can't be sure if it's alright now, cuz I don't really spend a lot of time w it so far, but seems like it's in a better condition...
Thats just how I dealt w it, u may wanna try it before going thru some xhausted steps such as restoring, etc? may be it will help? ne way good luck w that man