Similar discussion in SSHE
There isn't really a specific point you should slow down if you suspect an overset; it depends on reads which can also depend on the specific board and preflop action. For example, you should be a lot more scared with 22 on a 247x board if an UTG open-limper caps the turn, than if I have 66 and the board is 6KJx and someone who limped after several players caps the turn. This is both because two pair is more likely on the second board, and because even "tricky" players tend not to limp behind with JJ or KK (though I have run into JJ in this exact situation before in B&M's). Similarly an ace-high flop in an unraised pot is a good thing because of potential ace-rag two pair hands.
Generally I slow down only on the river if Villain caps the turn, or gets capped and bets into me anyway, but not before that point unless I have a specific read on that player...but that's in B&M's. In online micros it could be correct to cap the river every time; I don't play them enough to be sure. Again it's really opponent dependent but thankfully it doesn't come up that often.