Just as it was on the Xbox, the PC version is quite buggy. After about the 3rd chapter I started seeing crashes right as a cut scene is about to start. All you have to do is re-run the game it usually it picks up right at the cut scene so its not too bad.
Another bad bug is that some doors (especially in the end of the awakening chapter in the sinking ship) have very odd hit detection and will not let you through the door that you MUST GO THROUGH in order to progress. Usually I found that if I jumped wildly around the right side of the door eventually it would let my go through it. One door was unbelievably stubborn though and it took me quite a while to get through it.
There is also the issue of lock on. Its all kind of buggy. It locks on to the wrong objects and wont give up no matter what. Sometimes a reload will get you out of a bad lock-on but other times you have to run behind cover and turn the camera.
Despite all this, the game is actually good underneath all the bugs. And usually the gameplay is really fun. Its just a shame its tarnished by what was obviously a rushed game.

I'm having some of the same problems. Only, my game didn't make it to the third chapter. I made it as far as carrying Ethan down the hallways of the station when the game crashed. The first time, I got a General Protection Fault error.
As you said, I was able to load and play through the next level, whereupon it immediately crashed again, this time just giving me 'Advent.exe has stopped working'. And of course, no further details.
Nobody released a patch for this? This game seems buggier than a Louisiana swamp.

It is a bit crash-happy, indeed. Fortunately, the crashes are pretty random, and I couldn't find any crash that would stop you from progressing in the game. If it crashes, just run it again and go ahead.