Halo CE has been smooth sailing for me for the most part. I did get the same bug where it says you are going to the Library, but it is actually 343 Guilty Spark. It actually does not skip the level. However, when it did this, I exited the game and it said I had beat 343 GS, even though I did not beat it. So I just picked it and everything ran smooth.
Outside of some slowdown when using the Warthog on Halo and a few other isolated areas using a vehicle, Halo CE has been solid performance wise. Oh, I did have a audio bug where after you get the code/chip from Captain Keyes on the Capt Keyes level (not going to say what happens) but after that Cortana is going on and on that we need to get to the Captain because his life signs are depleting. Which was odd considering what you just did.
But it has been very solid for me. Starting up Halo 2 today.