You can get ceramic capacitors with similar voltage ratings, also polypropylene ones which may be a better substitute. But you really can't tell by looking and the original ones are probably perfectly ok. It is electrolytic capacitors which bulge when there is a problem with them. Oil filled caps are probably one of the most reliable types, working fine after many decades.
However in addition to what Unclejed says, there are a few other possibilities for the fault you describe.
First I would re-work all the soldered joints on the board, because you say the motor behaviour is erratic, it may be caused by a dry (aka "cold") joint, especially since the unit is quite old.
Check all the resistors. It's quicker than trying to do proper fault finding if one of them should be the culprit. On the other hand even if they all check out ok it doesn't guarantee there isn't an intermittent fault with one of them.
I'd check all those screw terminal connections too for dirt, corrosion, whatever.
You can get weird faults with old transistors and diodes. I would check to see if any respond to heat/cold whilst the circuit is running - well they'll all respond a bit but you are looking for a response that relates to the fault.
Preset potentiometers are another weak point as the wiper contact can develop a bad connection to the track. If you haven't already adjusted them, I would mark the positions and give them all a good tweak and maybe even a squirt of switch cleaner. You can use your marks to put them back in their original positions.
Other kinds of electro-mechanical fault include switches and relays. Again contacts can become corroded and cause an erratic connection. Switch cleaner is your friend. Check for corroded wires too.
With the unit powered on, check the voltages across the zener diodes, make sure they agree with the body marking, check if they vary whilst the fault is occurring.
Check the DC supply voltages to the circuit - are they stable?
Unfortunately you can't test the IC's without powering up the device and doing voltage checks on the pins. Find the data sheets for them so you know what pin does what, so you can make some sense of the readings.
If none of that helps, it's down to good old fashioned fault finding. Good luck!