Lemmix does have some glitches, although they just might be stuff like some glitches not working.
Apparently, there is a steel-related glitch that cannot be saved in a Lemmix replay.
To elaborate on the above:
This happens because the Lemmix replay format doesn't keep track of the lemmings under the cursor when the skill is assigned. When you run the replay, it tries to assign the skill as though that lemming was the only one under the cursor, but the glitch (where the lemming digs despite being on steel) only works if you have another lemming (performing one of a certain set of actions) under the cursor at the same time. Thus the skill assignment fails because the game detects steel under the lemming. The same applies to builders at the very top of the level.
Another thing that came up recently was the wall at the left side of the map. Lemmix doesn't detect terrain beyond the visible area, whereas DOS does. On a level where the terrain extends off the map, making a lemming block, dig or explode (start the "oh no" animation) at the exact moment where it turns around can produce different results in Lemmix to what you get in DOS. (Actually, getting different results with a digger would require a fairly specific setup, but I digress). Something else that crossed my mind is the possibility of editing a replay file to assign a skill to an off-screen lemming that can't be selected using the mouse.
Plus there's a couple of well-known ones - pausing for time and the nuke glitch.
Oh yeah, I guess those don't work... or at least the nuke, so I've read.
Can't pause for time in lemmix either, sadly...
News from the glitch thread...
Trapdoors have no inert trigger areas in Lemmix, but they do in DOS. See the
glitch thread for details on what these "inert" triggers are.
I guess that means Just a Minute is even harder in Lemmix!
I guess that means Just a Minute is even harder in Lemmix! 
Actually, the hardest is if you play such levels on the Amiga/SNES/Sege Genesis (Megadrive) versions. The DOS's clock seems to run slightly slower than Amiga. I've had people who'd been shocked when they played the versions where time runs out faster.
Oh great. And I kinda like the genesis version.
The one-minute frameskip doesn't work right when you hold down the keys to go forward several minutes. It starts taking off random amounts of time instead (less than a minute at a time, fortunately). This probably isn't of much consequence though

And I think the 10-second skip takes off slightly too much - maybe just one frame. It's more noticeable if you hold it down.
Something else that crossed my mind is the possibility of editing a replay file to assign a skill to an off-screen lemming that can't be selected using the mouse.
Actually you can already sort of do this without editing the replay file. I notice that Lemmix allows you to scroll the level a little further to the right compared with DOS Lemmings. Try Mayhem 30 for example. This would definitely allow you to assign skill to a lemming in Lemmix that you won't be able to do in DOS.
(Note that this does
not mean the level should've been clipped more on the right. Even in DOS on Mayhem 30, you can assign skill to a lemming that's no longer visible onscreen, as long as it's still within the "detection range" of the cursor.)
I was actually referring to the left side. By using a blocker to push the lemmings off the screen, then exploding it and blocking one of the off-screen lemmings when it comes within range of the cursor, you can push some lemmings even further to the left. Then you can't select them any more. (In Lemmix, that is.)
And now I've just tested this in DOS for the first time (

) and it doesn't work. The lemmings don't even go all the way off the screen...
I found another one. I added decorative terrain to one of my levels, and decided to test drowning in the water beyond the steel (I hadn't yet made it indestructable). There were no trigger areas there, but the lemmings still drowned.
Not sure what you mean there. Can you post a pic?
Too late. I already added the steel. Here's a good description, though.
L
|\/\/\/\/\/\/\/\/\/\/\/|
| This water here has no|
| trigger area..........|
L stands for "Lemming." The Lemming in the water is drowning, despite the lack of a trigger area.
I could slop something in Paint, though, if you'd like.
Wait, you've lost me. I was under the impression the water object itself was the trigger. How can the water have no trigger area?
Only so many objects (was it 16?) can have trigger areas in DOS lemmings, and the number of objects it supports and the number of objects that can have trigger areas are not identical.
This isn't exactly a "glitch in Lemmix", since it's something that also happens on DOS Lemmings.
Did you read all the posts? I was trying to explain a glitch I found in Lemmix... hmm... maybe I'll just show it off like this.
The pic has green water (I was using the pink tileset when I found this, but I'm using the green in this one (I don't know why)) and pink water (to represent the water with a trigger area).
Oh okay, yeah we know about this one, it affects even levels from real games (eg. Holiday Lemmings).
Oh, that. Yeah, I posted about it a while ago. This is what lets you solve "Check Your Hints!" by the first or second exit in Lemmix, when only the 7th works in DOS.
Here's an interesting but minor one: If you play a level, then exit on the results screen (not sure if you have to pass the level or not), then change to another difficulty rank, your position will still be changed. EG: Complete Fun 1, exit to the main menu on the results screen, switch to Tricky, and you'll start from Tricky 2.
Are you talking about the Lemmix Player here? Obviously this doesn't apply to the Lemmix editor.
And you didn't complete Tricky 1 before this happened?
This is the Lemmix player that we're talking about, and I have tried that and it works, which is rather nice because I can find a way to skip "Steel works" without cheating
Hey! You're not supposed to use glitches to entirely skip levels!