So far, there's been a couple of bugs and glitches during my first playthrough of Halo CEA. They are the following:
1. At the start of Halo CEA missions Halo, Truth and Reconciliation, The Silent Cartographer, Assault on the Control Room, 343 Guilty Spark, The Library, Two Betrayals and Keyes, the pause menu would pop up. I have yet to start the mission "The Maw", but I assume it'll happen again.
2. Character mouths do not move while talking in classic mode on Halo CEA. Some of these (if not all) characters include Sergeant Johnson and Captain Keyes in missions "Halo" and "Truth and Reconciliation".
3. After reaching the first facility in the mission "Silent Cartographer" on Halo CEA, there was a big shift in lighting while walking down the first ramp inside, looking darker than before. The lighting would continue to alter while walking up and down the ramp. This happened again after walking up and down one of the first ramps after activating the Halo-panel (same mission). This only occurred in Anniversary mode.
I have two Xbox recordings of these bugs/glitches, but I have yet to learn on how to add them. Don't judge, haha. Other than that, I hope I was helpful!