Why does my SWR jump around when I set up on wet sand?

Perfectly normal for a beach activation, and your buddy has it half right. Salt water is a fantastic conductor, but it only helps your antenna if the antenna can actually couple to it. Dry sand is one of the worst grounds you'll ever set up on, closer to an insulator than anything. So what you were seeing was the ground underneath you changing character as the tide moved. Dry sand, damp sand, wet salt sand, all give you different amounts of loss and different capacitance to the antenna, and the reading wanders as that boundary shifts back and forth under you. The wind was probably contributing too. Two loose wires lying on sand will get nudged around, and every time one moves or lifts you get a little change. That part settles down once you pin things down. On the radials, two short wires is relly the minimum for getting on the air, not a proper setup for a vertical. I usually lay out at least a dozen if I can, and I make them a mix of lengths rather than all tuned to one thing. On a beach the trick is to run a good number of them downhill toward the waterline, because that's where the good ground actually is. When the tide comes in and the wet zone creeps up the beach, more of your radials end up over damp sand and the antenna settles in better. If you're stuck with just a couple of wires, do what some of us do and pour a jug of seawater along the radial path. Sounds silly but dampening the sand around the wires makes a noticeable difference. Weigh the wires down with rocks or driftwood and peg them flat so the wind can't lift them. Also recheck the SWR at the same time of day relative to the tide if you want repeatable numbers. Half the confusion on the beach is just that the ground under you is a moving target.

Gotta push back on the jug of seawater thing. Tried that exact trick on a dune setup last fall and it was a waste of a perfectly good water jug. The sand drained and dried out in under half an hour with any breeze at all, and the SWR crept right back to where it started. You'd need to keep re-soaking the whole area every few minutes for it to mean anything. If you've only got a couple of wires, just add more wire instead, even sloppy lengths snaked around the base beat trying to fake a ground plane with a bucket of ocean.

I tried something like this at a lake once with a pole antenna and two wires and gave up thinking my little radio was broken, so this whole thread is kind of a relief. One thing I still can't figure out though. Do the wires have to spread out evenly around the pole like spokes, or can they all just run off in one direction if that's the only space I've got? Mine were kind of bunched togather on one side and I never knew if that mattered or not.

I keep a little log at my regular spots and my usual sandbar runs an SWR of about 1.5 at low tide drifting up past 2.0 as the water comes back in. Same rig, same wire lengths, nothing moved. Once you accept the ground is a moving target you stop chasing it and just log the reading with the tide time so you know what normal looks like for that spot.

To the lake poster, no, the wires do not need to be spread like spokes. All bunched one way still works, it just biases the pattern off to that side. On a crowded beach that can acutally be handy, aim the bundle out over the water and your signal follows it.