Something screwy with your Carrier voicemail settings then. Sounds like you have a messed up Visual voicemail or your phone is messed up. Try a restore first prior to calling your carrier, then it's their problem.
Sprint is my carrier and I have had sporadic voicemail problems for over a month. When I stopped into the Sprint store I was told it was a "known Apple issue" with the OS and a patch would be out soon.
I show a voicemail received. When I tap the message to play it, I sometimes (20%) of the time I get no playback. It shows a voicemail received, but with a length of 0:00.
When I call the person back, they tell me they did leave a voicemail.
The message is still there when I return to voicemail. It has a blue dot to the left of the callers name. When I select the message it highlights in blue and has an arrow where the dot was, like a "play" icon. Pressing this icon does nothing. Nothing.
Works fine the rest of the time. Frustrating.
Is Sprint lying to me or is this an Apple issue?