coin mechs can have 0-2 different adjustments.
the mechs pretty much work the same:
1] coin drops down into the top left
2] cradle tips the coin to the right while checking circumference
3] coin rolls right between a magnet and the back plate to check for slugs and thickness
4] coin hits right edge of frame and bounces back to the left. Checks weight
5] If it bounces far enough, it drops out the bottom left onto the coin switch trip wire.
the adjustment screw on the front - if there is one - changes the gap between the magnet and frame in step [3]. You want the frame surface to be clean, smooth and dry and the gap big enough for the coin to not wedge.
on mechs with no adjust screw, the magnet is sometimes mounted on a soft metal bracket that you can bend up to adjust the gap size.
if the mech is rusty or pitted, it may be easier to get another mech. They are generic for each coin size.
if you coin is not getting stuck but wants to fall out the return too much, there's sometimes an adjustable bar on the back side that sets the hurdle the coin needs to bounce over.
for the mech to work well, the coin usually needs to drop in with some velocity and the cradle needs to pivot easily. The cradle axle is the only place you could lube if it's sticky.
the lockout coil behind the mech needs to be powered and pull the armature away from the mech or all the coins will reject. If the coil is bad, you can stick some folded paper behind the mech to shove the armature back onto the coil top.
you can just stick your voltmeter probes on the two coil terminals. if you don't have 50V, that's your problem. If you do have 50V, the coil could be bad. Ideally disconnect one wire from it and check the resistance with an ohmeter. If it's infinite, look at the coil and see if the coil wire broke off the terminal. You can unwind a turn of wire and reattach if so.