It never crashed once for me. I heard trying to Chat might lock you in to a place where you have to close the game, but I never tried that I guess.
I heard there was a problem customizing the controls, but I had no problem there either.
The server browser is buggy, but it never prevented me from getting in to a game.
I played for hours without ever crashing.
As described by many, the game feels like MW2 written in the Frostbite Engine. That's exactly what some people are looking for. Others, not so much.
In previous interviews, the dev team said there would be lots of different game modes, so if this beta seems limited, it would be wise to reserve judgement about the finished product for later.