Do we need to add extra caps to both the input and output sides of the regulators, or just the output side?

RA: Both. There are multiple schools of thought on what gives the best performance, so its best to have both possibilities. The large electrolytic caps give good filtering of the low frequency stuff but also have a big inrush current when the supply is first activated. Even so, it would be good to have a pad available so that we can have a large-ish cap on the input and output with a 35V or higher rating. Its not necessary that it be surface mount - could also use tantalum. There's no need to make it larger than 100 uF.