Like the previous poster, tkamiya, I have worked on about 150 different HP pieces (from the 1970-1990 time period). But my percentage of faulty capacitors has been somewhat higher - about 10% of the pieces had faulty caps. Perhaps that is because I actively seek out and buy broken pieces so I can enjoy the challenge of repairing them. I would expect the faults statistically to be lower among all HP equipment.
From my experience, the small, silver colored Sprague electrolytics are the worst. The large "computer grade" electrolytics one usually finds after the bridge rectifier in the power supply have always been good. Occasionally, a tantalum capacitor will short - these are relatively easy to find when they do.
If I see one or more electrolytics spewing its guts out, or bulging a lot, I usually replace it. If it is on a board with a few other similar types, I usually replace them all. Capacitors are pretty cheap.
Oh yes, if you see any gold colored Rifa suppression capacitors at or near the AC entry point, replace them without hesitation simply as a precaution (they will eventually explode causing a smelly mess).