No matter how many different mobs Gary is controlling, I'm fairly certain he's obliged to play Traits for each and every mob before he begins his turn. However, I just saw words that nearly shattered my faith in our rule-abiding DM: Yellow Puddings discarded Death Meld. Yellow Puddings discarded Death Meld. This was in the discard phase during battle 3 (Coffins of Slime) of the adventure The Pools of Slime. It is true that the Yellow Puddings had not played anything yet on this round; however, I still don't think he's allowed to pass (and thus get the round to end) without playing those Traits. Besides, Gary had actually done other things this round: the Green Jelly had played the Trait Vulnerable, and the Zombies had moved. Oh, and I killed one of the Yellow Puddings, so its buddies really would have liked Death Meld to be played by then.
I saw this happen too. There was one Yellow Pudding left in the second battle of Viscous Tombs. At the end of the round it discarded Death Meld. In my case the Pudding in question already had a Death Meld attached. I've noticed that Gary never seems to play identical traits onto the same minion, I assume this is intended? And if so, is something about this rule overriding the must play rule? Although it sounds like that wasn't an issue in Sir Knight's battle, so maybe it's this particular card.
I also saw this bug; I caught Gary discarding a Vulnerable. Which, unlike Death Meld, I can definitely understand him wanting to avoid. I have seen Gary play multiple identical traits on the same character, though. :/ Is this a recent change you've noticed? Because I've seen multiple Death Melds cycle through the same slime before multiple times, I've seen Combustible played on the same tree at least twice in the same turn several times, and I've lost count of the number of times a Bronze Golem has cycled through all the Clumsy cards in his deck in the first turn.
I can't say that it was a truly scientific observation, just part of my feel for the game. As far as I know it only applies to minion groups. Individual enemies can and do play multiple identical traits on themselves just as we do, but I can't bring to mind an instance when Gary played an identical trait onto the same minion -- I figure there's some rule about distributing them lest groups draw three Vulnerables in a row and nullify two of them by using "no identical attachments" on a single minion out of five.