Halo CE:
-Truth of Reconciliation level. One time Captain Keyes decided to shoot the corpse of a Grunt he had just killed. It wouldn't have been so bad, except that he was wielding a Needler, and there were some plasma grenades sitting nearby. Needless to say, hilarious carnage ensued.
-The very start of the Silent Cartographer level. Your Pelicans drop the Chief and the Marines on a beach where the Covenant have the high ground instead of, oh I don't know, setting down on the FRIGGIN' HUGE LEDGE RIGHT ABOVE THEM.
Halo 2: The Prophet of Truth's plot to betray the Elites always seemed needlessly complex to me. Instead of wasting an entire advance fleet for the sole purpose of having the Prophet of Regret die by the Chief's hands, why not just quietly assassinate Regret, blame it on the Elites, and proceed to overwhelm Earth's defenses with a single huge fleet? That way he could proceed to uncover the Ark with no opposition. Also, all of the Elites seem to have suffered brain damage in this installment, as their ability to take cover and generally behave intelligently in a fight seems to have left them. They're much more likely just to charge blindly into the fray, and let's not forget the turkey shoot on the bridge in New Mombasa. If sending twenty Ghosts down a narrow bottleneck didn't stop the Scorpion tank, you might consider a different tactic instead of sending twenty more.
Halo 3: I realize the UNSC military's been thoroughly battered by now, but why do they have to drop nothing but light vehicles like the Warthog and Mongoose most of the time? I would have killed for some Scorpions backing me up during the first Scarab fight. Also, Miranda Keyes is a moron and a drama queen:
Trooper: Ma'am, squad leaders are asking for a rally point, where should they go?
Keyes: *Dramatic pause* ...to war.
That's it. She's asked a perfectly legitimate tactical question, and never bothers to actually give a clear answer. Probably her crowning moment of stupid though is when she tries to stop Truth from activating the rings on Installation 00. When Johnson tells her to quickly kill him and then herself so Truth can't use either of them to activate the controls, she hesitates, giving Truth the opportunity to kill her. Way to go, lady. I know you don't want to shoot Johnson, but the fate of the galaxy is at state. Be the soldier you are (or at least the soldier you're supposed to be) and fucking DO IT. Good thing the Chief made it in time thanks to the Flood's intervention. It's pretty sad though when a galaxy-threatening parasitic abomination has more common sense than a trained soldier.
Halo ODST:
Covenant: Hey, let's attack that elite squad of ODSTS armed to the teeth with rocket launchers and missile pods with incremental waves of easily shot down Banshees! That's bound to work!
Halo Reach: Tip of the Spear level:
Falcon Pilot: I don't think going through that Covenant shield's a good idea.
Jorge: *****, do what I say!
*passes through shields*
Falcon Pilot: We've lost all power. We're going down.
Jorge: NOBODY COULD HAVE SEEN THAT ONE COMING.
Also, why didn't the Covenant send in a massive invasion fleet from the get-go, given how they have a huge numerical advantage? Taking the planet would have been much quicker. In fact, the novel The Fall of Reach did just that, and the main battle only lasted a day (thanks for royally screwing the canon by the way, Bungie).
This isn't even going into normal screw-ups by the AI (Piss-poor driving, Marine vehicle gunners ignoring the Wraith tank to shoot at a fleeing Grunt, team-killing with bad grenade throws, etc.)