OK, posted this in the investor-only forums, did not know bug reports were public. Kudos for transparency, I guess!
When defeating watchmen, they get stuck with 1 or 2 HP, at which point they can no longer be damage but also no longer do damage. They follow me and my riflemen around making wooshing sounds, until they respawn at their original point. No loot and no XP obviously, and no progress on the first quest. Getting a second power that does burst damage has no effect on them, so it is not the riflemen that are bugged it seems.

The error seems to be limited to my Commander, or at least my fire tanker can defeat them. Will make more commanders to test this if no one else has.
Keep up the good work!

Updatification: Watchmen can be defeated and quest progression resumed by dismissing my riflemen and defeating a few watchmen using my own power. Also had to log out and back in to resume the quest. So, room for improvement here, but workaround is available. Keep up the good work!

Obviously everything is a work in progress but I found with Commander it was easier to start with Rifle Burst so I could kill stuff solo and then took Call Soldier for extra damage/protection. YMMV

AEGIS wrote: In that case, you would not run into this bug, so it is good weirdos like me are here to play strangely before release! ^_^
(Enjoying the class overall so far, very pleased you guys made it a priority to have commanders from the start.)

Can confirm, this bug only happens if a pet gets the kill shot. Then the mission does not update and the mob still looks active, but you can't use abilities on it and pets won't react to it. It can't hurt you either though, so I guess you're fighting a ghost

This only happens though, if you have a quest for which those watchman are updates. Pets can kill them without issue if you do *not* have a quest involving them.