For starters, it will not only be compatible with the spanking new iPhone 5, it will also bring with it fixes for Gmail on iOS 6. If taking the App Store route is not exactly your cup of tea for some particularly personal reason(s) of yours, there is an alternative – to do so from the update prompt that is within Chrome itself. Some of the known issues can be further read up on the Chrome support site. Needless to say, if you have a bug to report, you can always file it with the folks at Google, and hopefully, they will be able to get it fixed – and soon.