Yeah, this is something with Verizon tho... I noticed this with my Android phones (had Android 3.5 years before I got my iPhone 4s) -- and yes, I notice this on my iPhone 4s as well.
Basically, you aren't getting the "ringing" that happens on initiation of a call. If you stay on, you'll notice the person you called will say "hello?" after 5-10 seconds just because you didn't get the ringing to start with. This happened to me yesterday while calling a family member. I notice it's happening a lot more often these last few weeks.