I agree it seems likely that's why the video confidence test is failing.
I don't have the full 8590A service manual. Mine is missing the processor, A/D and other sections, so what I'm about to say here is somewhat blind. I do have a 859xE manual, which is similar, with many of the same parts with the same Uxx designations. If you know of a good copy somewhere, please point me to it.
So, caveat, caveat...
In the 859xE, the video filter is before the AUX VIDEO output. So, if it's the same for the 8590A (which it should be), I don't think it wouldn't be the video filter.
The 859xE A/D has a MUX (U64) which selects the AUX_VIDEO signal on pin 4. I would start there, and verify the you can see the AUX_VIDEO signal. As a sanity check, provide an input signal to the analyzer, and you should see the curve on that pin, without the glitches.
After the MUX it becomes more complicated, since you need to synchronize your measurements with whatever is going on with the MUX input selectors on pins 1, 15, and 16. With any luck, the system is not doing anything with the MUX while sweeping and it's always set to input #0 (pin 4). But you can check the MUX selector inputs for activity.
I would also take a look at the ADC itself (U47) and make sure the REF OUT (pin 9) and REF IN (pin 10) are stable. Check other pins to see if there's any activity that correlate with the glitches: +15V (pin 7), -15V (pin 11), +5V (pin 1), 10V SPAN (pin 13), BIP OFFSET (pin 12).
You also have a gain stage (U45), and a sample and hold (U46) which deserve some scrutiny.
There may also be some diagnostics which could help verify the A/D operation, but again I don't have that section. There is brief mention of a +10V and -10V reference check that is apparently described in the section I'm missing.
EDIT: "Wouldn't" --> "would", but hopefully the meaning was obvious anyway.