Two separate 'repair'/awful design correction attempts in this thread.
The DG1022 has a pretty noisy output. All the noise is above the bandwidth, making it pretty easy to remove with an LPF - though the bands are
close (within less than half a decade), requiring a good, precise filter. I've designed and tested a nice, inline output filter for it, seventh order Bessel with integrated common-mode filter, which puts the output noise down within the noise floor of my scope. I'll post more on that later - PCBs, BOM, plus I have a couple extras (first come, first served).
However, while I was characterizing it, I had to push something else onto my stack:
My Rigol DG1022U does this sometimes:

But sometimes, it even does
this:

The cause appears to be related to this, er,
special output amplifier layout:

I've confirmed that another unit does the first one, but not the second. A bit more later tonight on an attempt to fix it. Has anybody else seen output amplifier instability like this?