Looking at C1552 and C1542 they are both larger power capacitors mounted to the reverse side of the board. Are you thinking I should solder a capacitor to the bottom side (the visible side) of C1552 and hook my scope up to TP1548 and see if there is any improvement to the ripple? I assume the capacitor should be electrolytic with voltage rating exceeding say 25Volts or so? Any suggestion on the uF rating for this test cap?
It is a temporary connection to see if the existing capacitor is duff, so make connections any place convenient. Yes, that is probably directly across the end of the terminals that are visible without removing the PCB - and you probably won't be able to put the case on at the same time! (Since you are a beginner, I
won't suggest you simply hold a capacitor and touch the leads to the live circuit!)
What's the voltage rating of the existing capacitor? Any parallel capacitor should have the same or higher voltage rating.
Have a look in the manual at the tolerance of the capacitance value: that will give a hint a wide range is acceptable.
For the test (cf normal operation) the capacitance is uncritical. The larger the capacitor the easier to see the effect of having a good capacitor. Even if the capacitor is only 10% of the nominal value, you should see
some difference; how much difference will depend on how bad the existing capacitor is. But don't use a much higher capacitor value, since the inrush current might be too high. So, start with whatever caps you have to hand, say 10% to 100% of the nominal value.
If you identify problem capacitor(s), you will have to replace them with appropriate alternatives. Removing those caps is a pain, and you'll probably need "adaptors" to match the footprint, but that is a problem for later.