I've never heard of a single program running under 3.0 and failing under 3.1. Release 3.1 might be the most stable and bug-free version of classic AmigaOS available (when not hacked and patched beyond recognition).
The 3.1 installer will not completely purge your system. Most things will be left alone, but anything in danger of being overwritten will just be moved into SYS:OLD. This does mean you'll need to manually restore commands from the startup-sequence and user-startup.
Perform a backup to be 100% safe. This can be as simple as copying SYS: to a subdirectory on another partition.
