I have a similar problem with my iphone 4, as well, which started after I upgraded to IOS 5. After upgrading to IOS 5, I started to see a few issues, dialing and receiving calls, the two main features of a phone, and dropped calls. When I dial out, the iphone will sit in some state and the display shows "Dialing <person or mobile number you are calling>". It will sit in this state, at times, from 15 to 30 seconds before it decides to dial out. When receiving calls, there are times, (1 out of every 4 or 5 calls), the call will go directly into voicemail, without ringing, and yes the ringer is on. Also, on several occasions, the connection will drop just as I answer the phone.
Your first thought would be that I may have signal issue, which funny, because I thought of the same thing, but months before I upgraded the IOS. A few months back, my wife went into an AT&T store in Pleasanton, CA and mentioned to one of the sales reps about having bad cellular signal reception within the area we live in, which is in a new housing development. The sales rep gave my wife an AT&T 3G MicroCell device, which I installed in our, upstairs, master bedroom, next to window.
I wanted to mentioned the above just to rule out any signal or reception issues, because, after installing the MicroCell device, we have FULL bars, anywhere in the house.
Now on to the problem at hand, is there a fix to IOS 5, that solves this issue. There has been many occasions that I missed important calls, from recruiters, because of this issue. My frustration level has gone to a point where I have had the idea to take my son out in the backyard to play baseball and use the iphone as the ball.
I hope there is enough information for those of you who are adamant on getting details, but, if not, just ask.