Even though it is considered one of the greatest trilogies of all time, it doesn't mean there aren't any moments of stupidity.
The Fellowship of the Ring
In Elrond's flash back in the first film, Elrond tells to Isildur to destroy the One Ring in Mount Doom, which he ends up saying "No" since he was corrupted by the Ring. Isildur then starts to leave Mount Doom, while Elrond calls out his name, yelling, "ISILDUR!". You'd Expect: Elrond to take the Ring from Isildur and cast it into the fire and magma himself, since Isildur has been corrupted by the Ring, and thus destroying all evil. If he asks "Why did you do this?", Elrond could tell him that he (Isildur) was under the influence of the Ring. Instead: He does ABSOLUTELY nothing and lets Isildur leave Mount Doom, and he doesn't even try to stop him! Result: Because Elrond doesn't act to try to stop Isildur, evil still exists, the Throne of Gondor falls, and the Elves lose faith in the Race of Men! So technically, this whole thing is Elrond's fault, and yet he's never blamed for it! Evil was allowed to endure indeed!
In the film version of Fellowship Of the Ring, while our heroes are escaping the Mines of Moria, after Gandalf destroys the bridge to prevent the Balrog from following the Fellowship, as the Balrog falls, it uses its whip to try to take Gandalf with it. Gandalf hangs on to the cliff. You'd Expect: One of the heroes to go up to Gandalf and pull him up and save him. Instead: They just stand there and let Gandalf just fall to his doom. When Frodo tries to save Gandalf, Boromir holds him back.
The Two Towers
During the events of the film, Saruman ends up taking control and weaking Theoden, the king of Rohan. He has Grima Wormtongue be his sinister advisor. At one point Eomer returns with Theoden's son dead. Grima sentences Eomer to be banished from the town. You'd Expect: Eomer to put Wormtongue's head on a pike and take temporary charge until they at least figure out what the heck is wrong with Theoden. Instead: Eomer follows the order to be exiled, which significantly decreases the Rohan army!
The Return of the King
In Return of the King, Faramir led a charge to try to retake Osgilath from Sauron's army. Unfortunately it ends in failure with the entire unit wiped out, except for Faramir and his horse. Faramir is knocked unconscious from a poisoned arrow. Denethor however gets greatly upset and thinks he's dead. Pippin however noticed he's still kicking, but needs medicine, and even then Denethor ignores that, yelling "My line has ended!". When he sees Sauron's army at his doorstep, thinking Rohan will not aid him, he yells "ABANDON YOUR POSTS! FLEE! FLEE FOR YOUR LIVES!", which is stupid, so Gandalf knocks him out unconscious with his staff, and tells everyone to prepare for battle. Since Denethor is knocked out, this leaves Faramir's unconscious body unattended. You'd Expect: Pippin or one of the other Gondor people in the area to take advantage of Denethor being knocked unconscious by Gandalf, and take Faramir to the healers, and have him recover, thus saving his life. Instead: They completely forget about Faramir, and the fact that Pippin said that he needed medicine. Unfortunately, after Denethor regains consciousness, he still takes him to burn his unconscious body and himself in the Tomb of the Stewards, and none of the other soldiers even question Denethor and his suicidal madness, or ask "What if your son is alive?", or even check for a pulse on Faramir!
Just before that, Faramir reports that tens of thousands of orcs have taken Osgiliath, which he and just a few tens of soldiers have survived thanks to Gandalf's intervention. You'd Expect: for Denethor to listen to his son and realize that Osgiliath is lost for the moment, order the fortification of Minas Tirith and bring reinforcements and call for any allies that may be willing to come. He could also listen to Gandalf, who has proven to be a wise - if somewhat obtuse at times - and pretty much the one thing that can push the Nazgul back. And even if Gandalf supports Aragorn as King of Gondor, it does not mean that he cannot maintain his position, advising the king on important matters. Instead: he rebuffs Faramir's claims, saying that he and his men ran away because of cowardice, and orders him to lead a small army to retake Osgiliath (which ends up in the above What an Idiot situation). He also rebuffs Gandalf's quite sensible suggestions and rage about the fact that he'll never let Aragorn take the throne, saying that Gondor is his to rule. When Pippin, at Gandalf's prompting, lights the beacon that will call Rohan to battle, he gets angry with Gandalf. And, finally, when Mordor's army is at his gate and there is no one else in sight, he depressingly thinks that Rohan has deserted Gondor and Theoden has betrayed him.