Blizzard's mobile authenticator updated recently, and as soon as it did, we started getting tips on the tipline saying there was a major issue. Apparently the update reset the code associated with your authenticator, which meant that if you applied the authenticator update (and had the authenticator connected to your account), there was no way to actually get a code to login to your account. In short, if you apply the mobile authenticator update, you won't be able to log in to your account until you take the authenticator off completely (I'd assume you can then reinstall and reuse the authenticator, though people will probably be a little more trigger-shy about that one). There are instructions for how to do all of this over on the forums.
Of course it's a major issue, and in response, Blizzard has acknowledged the problem and apparently pulled the Authenticator from the App Store. So if (like me) you haven't updated yet, you won't need to worry about it, and hopefully the next version will fix the issue. But yes, if you have updated, you'll need to go through the steps above to remove the app from your iPhone and account, or just call Blizzard customer service at 1-949-955-1382 and they should be able to help you with the issue.
Update: So far we've only heard about problems with the iPhone version, and of course the issue is when you go from the old to the new version. If you use another phone, or have only used the new version, you shouldn't have any issues.