I'm nearly finished repairing my 3325A, so was interested to see curiousmarc in his latest video get one of two units going that he just got in.
My unit had intermittent front key activation as well, but that was alleviated by replacing the main 5VDC filter capacitor, so appeared to be ripple/noise related control issue rather than key contacts (but good to see a video of the front panel keys being accessed). I replaced the other power supply related electrolytics at the same time, to avoid future issues.
My unit then had function and cal problems, that was traced to some DAC levels not getting passed through to the various measurement circuits due to failed LM310 op-amps in the various sample-and-hold circuits. I had one spare LM310 so fixed the main functional signal, but waiting on another LM310 to come in to allow residual DC offset on the output to be auto-corrected. On the way to fault-finding, it can be worthwhile checking/trimming the analog circuit bias points as detailed in the service manual.
The heat generated by the main rectifier diodes, and the regulator devices is quite noticeable, and although likely not gross, can do with a check that mica insulators are given a thin grease smear. I didn't go the path of swapping the diodes out, or paralleling a 100V schottky, but that may be worthwhile for hot ambient use.