Alright. Maybe this one doesn't fit with the rest, since it's not really a physics-related glitch, but it's too interesting for me not to share, and after all, it is a glitch in Lemmings.
This one is on the Amstrad CPC version, and I call it the Cursor Glitch. The setup is rather specific but the execution is simple. Find or make a spot where a lemming is almost at or is going to the top of the level. The terrain can't go to the very top of the level, as it will act as a ceiling when climbing or building; it has to stop just before the top, so the lemming has just enough room to hoist or ascend. If you use the locking feature on this lemming, it should force the cursor out of bounds, or, if you're a couple pixels short, a digger or miner will nudge the cursor upwards (for some reason). Be sure to move your cursor or make sure the lemming dies before coming back onscreen or the glitch will end. You'll notice that the cursor is leaving a trail of ghost images all over the level at this point, and that you can't move it down (or possibly other directions, depending on the circumstances). These ghost images actually act as terrain, by the way. If you move the cursor directly upwards, it will reappear normally at the bottom of the screen and the glitch will be over. If you keep moving your cursor around out of bounds, you may cause some weirdness to happen. Move it in just the right way, mainly at the very top of the screen, and you will utterly break the game. Possible effects include ridiculous lemming counts, teleporting hatches and exits, ridiculously high time limits, missing or incorrect animations, severe graphical glitches, huge surpluses of skills, an infinite loop of binding your keys, and of course, crashing the game.
The effects depend on how you move the cursor, which skill or skills, if any, you assigned to the out of bounds lemming, whether you're playing on disk or tape, what level you're playing, and more. Below is a collection of examples of just what can happen with this glitch. They are all in Mayhem 1, but it looks like there are a few other levels where you can pull this off, one of which being Fun 13, where I got somewhat different results.
I would NOT recommend watching the tape version examples if you have photosensitive epilepsy! There are many flashing lights in the form of severe graphical glitches and loading raster bars.
https://youtu.be/l8W28Gq_4-8