I can only add that I've seen accuracy problems produce lobes in weird places on my little Chinese mill conversion. There are a variety of things that can go wrong but something I ran into (and why I don't like set-screws when I can use clamps instead) is where my lovejoy couplers worked slightly loose on the motor shaft. The set screw wasn't tight enough and so they "rocked" a bit and this looked like step-loss at times and backlash at others. To diagnose your problem, I suggest starting at the endpoint of the carriage and work backwards on every moving part - checking for tightness and wobble. Rhythmic noise is a dead giveaway too. Bearings and belts should be very quiet at the scale we are using. I'd also try cutting other shapes and sizes to see if it's always repeatable. It should be consistently visible in multiple things if it's a mechanical problem. Squares, circles, octagons, etc. Make them small and large to get a good feel for accuracy issues and if they always occur at the same spot in a curve or edge. For instance, a big French curve cut vector should also show the same issue as it will pass some of the same arcs but it's going to use different art and code. You could use your computer printer to print the image and then cut it in paper on the laser and hold them up together to see how close they are.
Also, if you have a
plunge-style dial indicator you can very easily test for backlash using the same process we use for milling machines. Attach the indicator to the side of the table somewhere so the head can touch it. Jog the head of the laser cutter so it is pushing the plunger on the indicator a good bit - call it 1/2" or so. Either note where the needle is on the indicator very accurately or just re-position the face so it's on 0. Now have the computer move the head away from the indicator for something like 1/4" or so. The indicator should show EXACTLY 1/4" movement. If you see less, then you have backlash, some mechanical problem, or are losing steps. The amount of backlash will be how much less than 1/4" it moved. The one gotcha for this technique is that when you are first moving the head into the plunger, you can't reverse direction. Every time you reverse direction, you are taking up the slack. So you have to get it to it's final position for testing by moving it only in one direction once you get close. This is a little hard to describe but should be obvious once you think about it a bit. This technique is the "tried and true" way to measure backlash for all axis on a mill, I've used it many times to dial in backlash compensation for Mach3. Good luck!
-Mike