We've just rolled out version 1.1.1 of Logos Bible Software for Mac. It is available for download through My Account > Order History. Follow the instructions from this blog post if you need additional help updating (it's an older blog post, but the same instructions apply).
Note: Version 1.1.1 REQUIRES Safari 4 and will not install unless Safari 4 is present. If you don't plan to update to Safari 4, you will need to continue to use 1.1. There are no differences between 1.1 and 1.1.1 apart from the version of Safari that is supported.
Version 1.2 is still underway, and we will inform as more details become available.