Last night in a match, my opponent took control of a region, and I sent a small force to recapture it.  I wasn't really paying attention when the units arrived because I had bigger problems elsewhere.  A few minutes later, I went back to that region to see why it still wasn't mine, and I found that I had two squads of brutes, and I believe once each archer and hermes (but I can't swear to the exact count of archers/hermes).  And my opponent had two medics.  My units were attacking, and the two medics were healing each other constantly back to full health.

It seems to me that 3-4 squads of T1 combat units should not have any problems wiping out a lone pair of medics, but for some reason it turned into a stalemate.

As a separate issue (but one also involving medics), in another match last night, I dropped a carving turret as I was marching through an opponents factories, and ordered my army to continue on elsewhere.  The army went, but 3 medics stayed behind and appeared to be healing the turret.  The animation was that they were traveling in the direction of the army, but then every couple of seconds they teleported back to the turret and healed it some more.  This went on for at least a minute, maybe two.  It looked just like I would expect if there was a lot of network lag between a host and client (and mismatched simulation rate), but it seemed like other aspects of the game were continuing.  I'm not completely sure what I was seeing, but it definitely didn't seem right.

Edit: wtfgrammarfail