Two Arbiters glitch

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

The Ark
Killing the Arbiter immediately before you activate the Cartographer will result in his duplication, though one of the Arbiters will leave as scripted. The Arbiter spawned outside the building at Mission Start and Rally Point Alpha is invincible. The Arbiter spawned inside the building can be killed.

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 he's scripted to, and after the second comes down from the Phantom, it won't have a waypoint above his head. The second one may 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

Four Arbiters
The Four Arbiters Glitch can only be performed on the Halo 3 level The Covenant.

When you have deactivated the third tower, run past the Flood, activate the elevator, and go downstairs. You will see the Arbiter and his Elites fighting the Flood. Kill the Arbiter and go to the entrance of the third tower. The second Arbiter will be spawned. Kill the Flood and go back to the first Arbiter. When the first Arbiter rises up and leaves the tower, go outside and you will see a Separatist Phantom. Destroy the Phantom. If you picked up a Fuel Rod Gun earlier, four shots will destroy the Phantom unless Tilt is turned on. Get the two Arbiters in the Warthog. Drive the Warthog to the Hornets. It is possible to drive to the Hornets without killing all of the enemies; any enemy that didn't die will be instantly killed except for the War Chieftain. After you have killed the two Scarabs, the third Arbiter will be spawned. Get the two Arbiters in the Warthog into the Citadel; drive the Warthog to the Citadel and stick the Warthog with a sticky grenade. After the Cortana Moment, kill the third Arbiter as you get the loading point. After the cutscene, get to the third bridge. There will be four Arbiters. To get the Arbiters to the end of the level, knock them off the platform and activate the light bridge. After the cutscene, the Arbiters will help you kill the Flood.

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 unaware of the Phantom's destruction and this Arbiter's continued existence, it spawns another Arbiter the next time the Phantom shows up.

The Four Arbiters Glitch works on The Covenant, when the Flood arrive on the Ark, since the game is scripted to spawn the second Arbiter when it cannot detect the first Arbiter. This is why when you choose not to destroy the Anti-air Wraiths, deactivate the third tower, and go outside, the second Arbiter will be spawned regardless of your choice.

Cloning the Arbiter by killing him prior to a cutscene is merely a manifestation of the Life After Death glitch.

Halo
By using a Spartan Laser with infinite ammo to kill the Arbiter immediately before the 343 Guilty Spark fight, players can create a "clone" of the Arbiter. Outside the Control Room, after the battle, one Arbiter will be standing around, and the other 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.