I ran a simple test model in MES with contact to check the stress output at the contact interface. The results make sense for elements without midside nodes but with midside nodes the stress levels are unusually high. I copied the first scenario to the second and added the midside nodes to the second scenario - no other changes were made. I did not test to see what happens if the node spacing is different on one part from the other. Attached is an archive file (renamed as a txt).
I have also had large stress variations at contact surfaces between the two parts - one part will show much higher stress than the other at the contact interface. Is this just a factor of 2D contact models with very few nodes in contact?