Not only am I having the same issue (first mission doesn't show complete, even though there isn't anyone left to kill), but now I can't even talk to Helena Blake. It shows I can talk to her, but nothing happens when I click space bar to interact with her. It's totally corrupted on my end.
Uninstalled from Steam, then re-installed from Steam (even made sure to delete "C:\Program Files (x86)\Steam\steamapps\common\Mass Effect Legendary Edition" folder). Steam kept the save game files. Now it's worse. Now, I can't even enter the building that Helena Blake is in. Even went back to a prior game save. At this point, I'm just going to live with the fact I can't finish this quest. I'm not starting from the very beginning, since I don't know how far back I need to go to fix this quest. (not willing to load each saved game point, just to see if that spot is a good version).
Try to repair the game.
(Origin > Game Library > right click MELE > Repair)
(Steam > Game Library > right click at MELE > Properties > Local Files > Verify integrity of game files.)
