I am also having problems with my Galaxy Nexus. I just received it yesterday and the signal goes crazy, all bars, to no bars, 3G to 4G then nothing. It drops calls every 5-10 minutes as well. It seems to be constantly searching for signal.
Now that I have said that, I will also say that I own a Verizon iPhone 4 and a 4S. Neither have connection issues while the Nexus can't even get on 3G. I have tried going to several places, including right across the street from a Verizon store. The Nexus still continues the behavior that was mentioned above while the iPhones are fine.
Was really wanting to switch from iPhone to Android, but I am really disappointed right now ;-;