Based on the schematics and help from an electrical engineer (thanks, ZFM), here's our analysis of what's going on:
On the Lisa video board, the horizontal phase potentiometer controls the amount of feedback to the input of the circuit that amplifies the horizontal drive pulse. A +5V line is connected to this feedback loop, which is generated on the video board from the +12V line coming from the output of the power supply. If this +5V line (and by extension, the +12V line from the PSU) contains noise, this noise will manifest itself as the horizontal phase potentiometer being quickly adjusted when the spikes in the noise occur. The user will see this as a jittery display, as the current scan line being drawn on the screen will be shifted horizontally when a spike occurs.
Therefore, this jittery display problem points to noise on the +12V line on the output of the PSU. The +12V supply is smoothed by several electrolytic capacitors: C14 and C15 filter the +12V line directly; C18, C19, and C21 filter the +5V line, which is coupled to the +12V line near the output.
According to the Lisa Hardware Reference Manual, the +12V line is designed to supply a maximum of 2A, and the +5V line is designed to supply a maximum of 8A. If these filtering capacitors are old and not performing up to their original specification, or if the capacitors have been replaced with capacitors that have an insufficient ripple current rating, they may fail to completely filter out noise on these lines.
My electrical engineer friend recommended that I replace the six 16V 2200uf capacitors in the PSU with capacitors that have as high of a ripple current rating as possible, in order to smooth out as much noise on the output as possible. I ended up ordering these:
https://www.mouser.com/ProductDetail/667-EEU-FR1E222L
They are rated for 25V (a safe step up from the 16V originals), and they have a relatively high ripple current rating of 3.63A. My original replacement
capacitors (installed in the PSU when I noticed this problem after recapping) had a ripple current rating of only 900mA. After replacing the capacitors noted above with these stronger replacements, my Lisa now displays a crisp screen. :lisa2:
Sunder - I think this fix would be a useful thing to add to your FAQ on the subject, especially if blusnowkitty attempts it as well and it solves the problem for them. Compared to the recommended modification currently on the FAQ, it addresses the problem at its source in the PSU instead of accounting for it down the line on the video board (so the fix can be carried between systems), and it does not require the user fixing the Lisa to expose themselves to the high voltages and other dangers of the video circuitry and CRT.