I've been having endless problems since I upgraded to the IPhone 4. I only got the phone on Friday, a couple of the problems have been resolved, but now there's 2 new ones.
First, the phone no longer rings. The only thing I did was to change the ringtone, and now it won't ring at all. I changed it back, and it still does not work. I've played with settings, ringer volume is at max, etc. I've missed several phone calls because of this (didn't feel the phone vibrate in my pocket -- seriously -- but when it's on a light table, I hear the table vibrate).
Second problem seems to only happen on some screens -- it doesn't always respond to my touch. I have no problem working with a calendar app, creating new appointments, or using the pop-up keyboard. But trying to change settings, turn a switch on or off, editing contacts can often be a study in frustration.
Another problem that I'm not sure has been resolved or not (as I've only had very short phone calls since the problem last struck) is dropped calls. After some research, it seems that this is a VERY common problem with the IPhone 4, yet the tech I spoke with was clueless. My previous Verizon phone was almost perfect so far as making phone calls. This one has been a nightmare. There was some kind of firmware update that was done during the last call to tech support, so I can't tell you if that fixed the problem or not. But at this point I'm ready to change phones. It's a piece of crap.