Bicycle Mechanics - Is my freewheel shot - and other questions

<for short version skip to next paragraph>
A friend gave me this old Diamondback Outlook, and I'm tuning it up to give it to another friend. So far I've replaced the headset bearings, removed the rust from the chain and relubed, tightened a loose shifter cable, bent the bottle cage (that was interfering with the FD), made a few fitting adjustments (bikes a bit small and he's bigger than me - so this will be interesting), "tweaked" the shape of the front derailleur using a wrench as a lever. I've taken off the pedals and plan to disassemble, clean, and regrease them today.
</skip>

I'm not really planning on doing anything else to it, but I've noticed if I hold the back wheel off the ground and get it spinning while the crank is stationary, the freewheel doesn't really hold still. It sort of wiggles around a bit as the wheel spins, even though it's not spinning itself. Does this mean it's shot? Is it unsafe to ride, or should it be okay?

Also, is there anything glaring I've missed that I should check before I pass the bike along?

The wobble is normal. I don't like it but even my new 7spd IRD does it. I have several old Suntours that are very straight but they don't shift as well as the IRD

All freewheels and freehubs wobble. If they don't wobble, they don't free spin.

All freewheels and freehubs wobble. If they don't wobble, they don't free spin.

He's talking about runout, not play. Most freewheels and even many freehub cassette bodies have runout.

And play can be eliminated from cassette bodies by taking them apart and removing a shim or two. You can almost always remove play without making them tight.

Good. Finished rebuilding the pedals last night. That was a pain in the rear. I think it's now ready for it's new owner.

He's talking about runout, not play. Most freewheels and even many freehub cassette bodies have runout.

And play can be eliminated from cassette bodies by taking them apart and removing a shim or two. You can almost always remove play without making them tight.

+1

All freewheels have runout. It's caused because of mis-alignment between the axis of the freewheel and the spinning hub shell. It's virtually impossible to perfectly align two threaded assemblies, so to rotating shell causes the wobbling effect on the stationary freewheel. It's similar to the wobbly feeling you get when riding a bike with a bent crank or pedal spindle.

It's probably fine and quite normal to observe this. The bearings in a freewheel and a freehub (not the hub itself) are the most lightly stressed bearings on the entire bicycle. They don't do hardly anything at all until you *stop* pedaling.