To me this looks like you "only" have a problem with the vertical. There is some additional signal overlaid on the sine wave. In the faster timebase settings, this also translates into a horizontal wobble -- but probably only because the trigger point changes, due to the added signal.
I am not familiar with your particular model of scope; others may have more specific hints. As a general approach, you should first aim to determine whether this problem is in the scope, the signal generator, or the wiring. Some ideas:
Does the problem show up on both scope channels, or one of them only? Have you tested the function generator with another scope, and know that it is good? Have you tried different probes or BNC cables to connect the scope to the function generator? Does the vertical wobble also show with the scope's built-in square wave?