I'm not sure exactly how many, but I can't open any threads with more than around 170 replies.
What happens is, when I open a thread, there's a slight pause where my browser window (Firefox) appears to crash, but then clicks out of it and the thing fully loads. It's barely noticeable when there are fewer than 50 replies, but after that it's basically roulette as to whether a thread will crash my browser. If I'm quick and hit 'stop' just before the pause appears then it can be OK - it seems like the main page is loading (all the replies are there) but DiS is then trying to load something extra on top of it that's crashing my browser.
I have no idea if this is happening to anyone else. It doesn't happen in IE, and the problem is a lot worse if I turn off adblock.