Easiest way to hunt for oscillations is to use AC coupling, and start with 
100mV/division, and 100usec/division. The exact frequency of the 
oscillation isn't important; what you want is less than 100mV peak-to-peak 
of noise. If you see 60Hz noise, either your 'large' electrolytic cap 
(usually > 1000uF)  is too small or it dried-out. To get rid of 
high-frequency noise, start with small bypass-quality caps, around 0.01uF 
as close as possible to the regulator inputs & outputs. Large caps have 
parasitic resistance and inductance that limits their ability to attenuate 
higher frequencies compared to smaller-size (hence smaller-value) bypass 
caps.

BTW, the 475 is a very nice analog scope; when I was a tech in the 1980s, I 
debugged a lot of computer boards with a 475.

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