I haven't been able to test the cel network, but after about 2.5-3 hours of heavy web surfing and general dicking around (settings, syncing, maps, launching various apps, camera, etc.), I had about 65% battery remaining, which would infer somewhere close to 8 hours of constant-use battery. That also included some "calls" to Verizon trying to activate it, I'm not sure if those calls were going over WiFi or the cel network or what. Not too bad if the % is accurate. I did notice the phone gets pretty hot under heavy use, much hotter than my 3GS did.
Your example doesn't sound right at all, something is wrong there. I'd completely drain it until it dies, then do a full recharge and see what happens.