After upgrading to IOS 7 I have had tremendous trouble with voicemail:
1) Calls going to voicemail without ringing
2) Not being able to access voicemail
3) Unable to change greeting as this function freezes the phone repetively causing it to reboot. THIS IS HUGE PROBLEM
4) The service reception seems to have significantly declined since IOS 7 update as well. Calls are being dropped more frequently
I live in 28655 zip code