Two Arbiters glitch

The Two Arbiters Glitch is a glitch] that can be exploited in two Halo 3 Campaign levels: Halo and The Covenant. The glitch, which can only be performed in single-player, causes the Arbiter to be duplicated for a portion of the level.

The Covenant
When you have de-activated the third tower, get in the tank before the Arbiter gets in the Phantom and blow it up while he's in it. The Arbiter won't leave the level like scripted and after the second comes down from the Phantom it wont have a marker above his head. The second one will then be teleported when you get to certain parts in the Citadel.

Another method simply requires that you kill the Arbiter just as Truth starts speaking, immediately before the cutscene when you enter the Citadel after defeating the two Scarabs.

Explanation
The glitch works on The Covenant because when the Phantom begins to engage its Active Camouflage, all of the Elites on board are removed from the level, as can be seen by players who actually get on the Phantom with the Elites. By destroying the Phantom, a player performing this glitch stops the Phantom from engaging Active Camouflage, which prevents the Arbiter and the Elites from being removed from the level. Therefore, the Arbiter remains with you. As the game is blissfully unaware of the Phantom's destruction and this Arbiter's continued existence, it spawns another Arbiter the next time the Phantom shows up.

Halo
The first step requires you to be able to kill the Arbiter right before you enter the room where the battle with 343 Guilty Spark is fought. In order to achieve this, you will have to do the Spartan Laser Glitch, and you should probably try it on Easy.

Once your Spartan Laser has been glitched into having infinite ammo, go to the door immediately before the fight with 343 Guilty Spark, but don't enter. Shoot the Arbiter with the Spartan Laser until he dies. Quickly after that, go through the door and initiate the cutscene. Once you finish the fight with 343 Guilty Spark, go outside and there will be two Arbiters. One will be standing, looking at you, and another will already be attacking the awaiting Flood; the latter has the waypoint above his head. Once near the end of the hallway, both Arbiters will stay back.

Explanation
The most likely explanation is that the Arbiter is removed from the level after the cutscene, to prevent him from trying to interfere (by, say, shooting at 343 Guilty Spark from behind a wall). After 343 Guilty Spark dies and the door re-opens, another Arbiter is spawned. Somehow, killing the Arbiter prior to the cutscene prevents the game from removing him. It may be the same glitch as the glitch that allows you to keep Sergeant Johnson alive by killing him prior to the same cutscene.