I get message "visual voicemail is currently available".

Available or unavailable? IF unavailable, it usually means you need to enter a passcode for vm or you aren't currently set up for it, but you can resolve both issues by contacting your cell phone provider.

I have the exact same problem on my iPhone 5, which also happened after latest update. I have tested to see if VCM is unavailable, but it works fine. Sometime toggling airplane mode on and off clears it, otherwise rebooting phone does the trick. Keeps on happening.