Got the game a few days ago and I also got this glitch.
I first noticed it on the first rain level. Thought maybe my TV was going bye bye or something, or if it was suppose to be like that...but then that developer would be seriously f.... up, if that was the case

Now I know that grain isn't suppose to be there, and now I can't get myself to keep playing and enjoy the game.
I tried the restart level thing. Only worked once with the central level, inside where you fight the thing from War of the Worlds.
At times square, no matter what I did, it would still be there.
I just created an account here to get my tiny butt seen, in a hope that Crytek will fix this, quickly.
If not, then I'm seriously gonna be careful on buying games from you guys in the future.
Since Far Cry 1, I have hold you guys together in a group with, id, valve and epic. How the game is in this state, is really making you, crytek stick out from that group. How something like this could get past testing is unbealiveable.
On a little sidenote...I normally don't buy that many games at their release, cause I wait for them to drop in price and wait, for patches to fix most problems with a game. And the last one, cause why should the first supporters of a game, get to be the guinea pigs?
So I finally go out and get Crysis 2, cause it's from Crytek. And I get punished for buying the game at release.
Exact same problem i had, Times square was literally unplayable, This happend 4 days ago and i havent played single player since because the grain completely ruined it.