Actually, if you're doing
no-chill brewing inside a sealed vessel like a plastic jerrycan/aguatainer that you put the wort in while it is boiling hot and it vacuum seals as it cools, protecting the wort, then nothing....you're fine. They've been doing that in Australia for decades, and here for a few years.
But if you're leaving it in an un-vacuum sealed vessel, like your kettle or something, then what will happen is that around 130 degrees or so, lactobasillus will take hold and your wort will become sour. This is one of the tricks in making sour mash beer, it is what you do on many of the guiness clones, you pull a measure of hot wort, and let it cool, allowing lactobasilus to take hold.
As for the the stuff vespa and homebrewdad mentioned has actually largely been discredited/disproven BECAUSE of no-chill brewing. None of those supposed issues show up on no-chill beers. That has largely led folks to believe, at least in terms of a vacu sealed vessel, that proteins preciptate out just fine and the beer is not cloudy either.
The no chill brewing thread is an historical hoot on here, because all the nay-sayers where coming out where all manner of supposed "Issues" like botulism and such, while folks kept saying, that it's been done for decades in Australia and noone's died, yadda yadda yadda....
And finally some Aussie brewers IIRC came in and told everyone to shut the Hell up, that if all those nasty things were happening did we think they'd still be doing it that way? And then after that, and people starting testing loving it, folks came around.