Yeah, I know I don't have an overcard here. I was just giving an example of times you continue drawing in big multi-way pots.

Big mistakes are characterized by ones that cost you many bets or occur often. If I didn't improve on the turn, I'd fold. I would have lost 1 SB there. If my improvement still made me a second best hand, I'd lose 3-5 BBs (assuming I don't overplay it like here). If I folded when I had the odds to continue, I would have lost more than 12 BBs.

Just because this time he had KK doesn't mean in the majority of situations the PFR will have AA, KK, or AK here. And those are the only situations where I would improve to a second best hand. Only 2% of his possible raising hands include AA, KK, AKo, and AKs. There's at least another 5% he'd raise in that position (I'd raise another 10% in that position - so this is quite the conservative estimate). And because the flop has both an A and K, there were less aces and kings dealt to players making it even less likely he has AA, KK, or AKo/s.

Fold the flop. You don't quite have the odds to continue after discounting outs here. It's a marginal mistake, to be sure.

What outs am I discounting? Perhaps one out in case of a flush draw. That'd still give me the outs to continue unless I knew for a fact he held AA, KK, or AK. I don't see the point in giving up these hands in big pots when you're likely drawing live and have the odds to continue. In a smaller pot I'd easily give it up since I wouldn't have the odds or implied odds to continue.

At least we all agree I overplayed the river (and perhaps turn).

It's not just the flush outs you need to discount. It's also the fact that you may hit a "clean" out and still lose the hand, and your lack of position can and will cost you extra bets when you are behind. The "5" outs to trips and two pair are worth more like 3 or fewer here.