Two points:
Barry's 2465B and mine have very similar issues with non-linearity on ch1 and ch2 but ch3 and ch4 OK. At least on my scope the power rails are ok for voltage and ripple. I also checked the power supplies where they have common decoupling to U100 and U200 and so far have not found anything amiss. There are threads here and elsewhere suggesting U400 as a possible cause and it's price is consistent with it failing frequently! I haven't yet checked U400 bias current or the voltages on the channel select inputs.
Secondly, Barry has several noisy analogue controls, DAC stability could be a common cause. Do the y and t cursors move smoothly? If they don't then it would be well worth checking the DAC output, there is setup procedure near the beginning of the calibration section of the manual that puts the DAC output on one of the DIP header pins and it responds to cursor movement - should be a good test.
Meanwhile my replacement U400 has been stuck in transit for over a week en route to the UK!
Roger