I am having this same issue too. I am new to owning an iPhone--just got it last week. My voicemail is not working. I see that I have new voicemails after I miss calls, but when I call into my voicemail account, it says I do not have any. I have spent hours on the phone with AT & T trying to resolve this, to no success. Today, the AT & T rep told me that "because voicemail is currently a free service with AT & T that I am not paying for, they could not offer me any monetary reimbursement"--even though I have been missing work and client voicemails.
So frustrating. It's listed as a "working issue" with no known date for resolution.