While Grenade Launchers, Plasma Repeaters, Plasma Launchers and jet packs were available in Halo: Reach, there is no explanation as to why none of them are available in the official first Halo game when either weapon could have easily been transferred among the appropriate parties.
Many of the firearms featured in the game - both Human and Covenant - never existed before the first Halo game, yet made their first introductions in later Halo games, even though Reach is a prequel to the first Halo. Bungie stated that the weapons were "lost" afterwords. The DMR was a prototype for the Battle Rifle
While Brutes were among the ranks of the Covenant and were frequently deployed in Halo: Reach, they were never used in the first official Halo game, only in Halo 2 where the creatures were first introduced, however, in the books they were actually the first sign of Coevenant species seen. In Halo Wars, they were also seen.
The sub-species Covenant race of Skirmisher has never existed in previous Halo games up until the prequel, the Skirmisher is another species as a Jackle, and Bungie said that those were the last of the Skirmishers; on Reach.
The goof item below may give away important plot points.
During the epilogue of the mission in New Alexandria, Kat is killed by a head-shot from a Jackal sniper. This would be impossible as the notable shielding on MJOLNIR armor that she wears would take the brunt force of the shot.