Under Windows, Sweet Home 3D should work from XP to 10.
Under Mac OS X versions where only Java 5 is available, the main limitation is the navigation arrows in the 3D view as you noticed (but the help about the 3D view explains the various ways to navigate in the 3D view). However, there could be some other small problems simply because I generally perform just a quick test of Sweet Home 3D under Java 5 with an old iBook G4 from time to time.

As explained here and elsewhere in the forum, the Advanced Rendering Plug-in doesn't work with Sweet Home 3D from version 3.4.
Some other plug-ins might not work if they require some access to local disk system and you use such plug-ins with the Java Web Start version (like the Copy as new furniture plug-in). Of course plug-ins must be compiled with Java 5 target to work under a system where no Java version better than version 5 is available.