It looks like there is some play somewhere. It looks like the circles are completing but something is sliding during the process to make it off.
It is pretty much pointless to go 0.1 for the resolution. Most lasers' dots are .1mm in diameter, so setting it to .05 will just make the job longer with nothing really gained.
Being that you are just sending shapes, so it is going by vector (and not raster), the line on the square is concerning. The x axis should not have been moving for that leg on the left to jiggle the line like it did. Is your laser on something like a workbench? If so, you do not want to be working on the other end banging around. I looks like your engraver got jostled.
Another thing that may help is to add vibration dampeners to your feet (ie - furniture cloth foot pads) and to find a way to secure your engrave to the workspace.
***EDIT***
Also, check your cables. Make sure they are all moving freely and nothing is binding. your laser module could be getting pulled around.