I own two 629-1 4" revolvers, one of which I just bought used. The other I've had for about 20 years and used a lot.
S&W 629s are far from fragile, but they do wear under heavy use and aren't suitable for loads in excess of manual-recommended maximums.
When inspeciting a used one, I suggest that you carry feeler gauges and measure the cylinder/barrel gap and the end play. The gap should be around .004 to .008 or so (smaller means likely you'll have significant end play), and end play ideally would be close to zero. End play is easy to fix by installing some shim washers you can get from Brownells, but it's an indicator of the amount of use the revolver got.
Next, check the tightness of lockup by feeling how much the cylinder will wiggle (rotationally) with the hammer cocked, and with the hammer released and the trigger still pulled back. Do that for each chamber. A little play is OK, but snugger is better.
Then to see if the timing is good, drag a finger on the cylinder as you cock and release (slowly) the hammer to see if the cylinder actually locked up. If it didn't, you'll be able to back the cylinder up with your finger. This one is pretty important - even though the revolver might be safe to shoot as is, it's nice to know that everything's in battery when it's supposed to be.
Those last two things are also fairly easy to fix, or a gunsmith can do it for a couple hundred dollars (here in SoCal).
Check the bore. Have the guy at the shop clean the barrel and forcing cone in particular. Chambers, too. Look at the forcing cone for wear or polishing that is on one side only. Look for cracks (unlikely). Look in the chambers, now bright and shiny, for any swelling or unusual marks.
While you're doing all this note the ease of opening the cylinder. It shouldn't take excessive pressure on the thumbpiece or be difficult to push open.
Look at the joint between the frame and crane, up front. If there is no gap at all, that's the best. If there is any gap, it should be tiny. A noticeable gap means abuse by the previous user.
Dryfire double action very slowly. S&Ws have a DA pull that increases resistance as you pull, building to a noticeable high point just before release. The whole pull should be smooth however, with no distinct steps. It should release crisply.
Look at the hammer and how it fits while at rest. Spaces on either side should be about equal. If they aren't, cock the hammer and look for rub marks on the sides where it's contacted the frame.
Look at the rear sight. It should be complete and the blade itself should have very little wiggle. The notch should be about centered on the top strap. The barrel rib should also be centered on the top strap, and the front sight not obviously bent.
-Don
