Algodoo

The glitch is actually caused by making things too big
The problem appears when your machine is very far from the center pos [0.0,0.0]. When a car is, say, 10 times bigger, you'll want it to go 10 times faster so that it looks like the real counterpart, but it'll travel tenfold. The farther from the center the worse the problem is, but the problem is that once you've gotten that far, you can't just get everything to [0.0,0.0], it won't fix itself automagically.
One thing you could try is copying everything and moving it to a new scene in the proper position, maybe it'll get fixed, idk

FYI your scene is like on [-5400,0]

Another thing: I'm always very paranoid about this, but one thing you could try is undoing sim start after you test your things. So for example you're making a gun, and you want to test it: you start the sim, then you load/cycle/fire, and after that you just open the undo dropbar and select "Undo sim start". That will ensure perfect grid alignment which is mainly why i do that

Start using 1:1 scale! at least for cars

Thank you for your advice! I just made my first scale car, a 1967 Alfa Romeo 1300 J. This time the car shakes and slides because of the wheels (density) clipping through the plane. But it's a start!

@The_Linkage, My Alfa Romeo has also now started to creep when I adjust sliders in the scene, and it's x position is fairly close to the origin.