I just purchased the MH 721-MK2 Plotter and am running Corel Draw X3 and have only been using it for a week (Christmas Gift) and I too notice that I'm getting these tags at the start and stop of the cuts. It sounds like the same "overcut/blade offset issue you are having...is it the same? It has really affected my weeding and tears.
I am considering editing the vector lines to overrun each other, but this would take quite some time...I have already edited to make rounded corners in some cases to make weeding easier.
Jerry