Just picked up a used Saratoga 4 person hot tub and am having the following problem

There are 5 jets in the tub, plus one small one on the bottom (appears to just be a small flow of bubbles, no real pressure) two of the jets will produce bubbles (but only one at a time), but 3 of the jets only force out water.

When I turn the diverter valve there is one jet, plus two "waterfalls" that come on behind two of the head rests, the one jet puts out bubbles, the other 4 jets are off.

If I turn the diverter valve the other way, the other 4 jets come on, but only one puts out bubbles. None of the jets are very forceful.

The other concern I have is that something just isn't working right - when I push the button for the jets, nothing really changes. I half wonder if it's only circulating, and not actually turning the jets on completely. The system is a pnumatic system, and neither the jets nor the lights work on the pnumatics from what I can tell.

Any thoughts on where to start with this?

You should notice a big difference between low and high speed. Go to the pack, and if any of the air tubes are long enough, cut off a small section, attach it to the pump barb and use your mouth as the air button. That will take the buttons and tubing out of the equation and is an easy first step.

I wouldn't worry about aeration until you're able to get high speed working.

You nailed it - the pump wasn't kicking in to it's second speed. A quick check of the air line revealed a blockage, and once I cleared that, it spun up great. There's still two jets that don't appear to be getting aeration but I'm not super concerned about those. Also, I'm going to pull off the side panel and replace the light bulb, as I'm guessing that the bulb may just be burnt out (cheap quick fix, right?).

Another question - I appear to have a slow leak - one drip every 3-4 seconds underneath my deck. I'm not really concerned about it right now, but I'll probably want to track it down this srping. What's the best way to do that? It's a fully insulated tub, so there's no plumbing that's exposed that I can see.

Check around the equipment very thoroughly. You shouldn't have any moisture. If you eliminate the possibility of the leak coming from the equipment, you'll have to get as close to the leak as you can visually and then start chipping away the foam, following the water.

The bulb replacement is indeed an easy fix, as long as there's power getting to it. You could also have a bad button, tube, switch, or transformer, so test the power before you order the bulb.