Congrats for the great scope!
What do you mean with "The screen displays a trace that's vertically wider
than the screen"?
Is it a horizontal trace that is so thick to occupy the whole screen
Is it a vertical trace that takes most of the vertical dimension, which
moves horizontally across the screen (and movement is noticeable on slow
sweep rates as you said)?
In either case, it may be vertical noise (or a frequency) that looks like a
thick trace simply because it's not in sync with the sweep. If it's pure
noise (white noise) that is finding its way into the vertical amplifier (or
originating on the vertical amplifier itself), if may be doing so at a
point past the point where the trigger signal is picked-off so she won't
sync on it no matter what.
If it's a particular frequency, even without syncing you may be able to see
waveform by playing with the sweep's Variable control, but if it's pure
noise and not synced, it may be impossible to see it as a waveform at
highest sweeps (and you will see always a "thick" trace) and at slow speeds
you will only see a vertical trace moving horizontally across the screen.
It may also be an unfocused trace (a focus problem), but then at slowest
sweep speeds, the vertical trace will be horizontally thick as well.
Can you post a picture of it? (On the Tekscope's "Photos" area, as the
pictures doesn't get through inside the messages)