The Death Star is the ultimate example. It's enormous, cost an insane amount of funds and manpower to build and operate, and it's only advantage over large capital ships like Star Destroyers is that it can wipe out entire planets (as opposed to putting down a rebellion while leaving the population and economic centers mostly undamaged), costing further quadrillions worth of economic damage with every shot, and in doing so, promote justified fury and rebellion against the Empire for such crimes against sentience.
The Imperial Walkers from The Empire Strikes Back are pretty impressive to look at, but when you think hard about it they're just huge sitting ducks for enemy weapons, and the Rebels manage to disable them just by wrapping cords around their legs and tripping them. What happens when the Rebels decide to arm themselves with some serious firepower, like the proton torpedoes they use to kill starships with? This article from Cracked.com points out some of its egregious design flaws. Unsurprisingly, in the EU, they're even bigger targets. Isard's Revenge has four X-wings take down four AT-ATs in as many minutes and take no damage at all).
That droid missile from the beginning of Revenge of the Sith that targets Obi-Wan's craft. They fire a missile at a ship. It overtakes his ship and opens. Then droids comes out of the missile and start dismantling the ship. This process takes several minutes, and gives Obi-Wan time to tell Anakin what's happened, who then tries two different strategies to successfully save him. The droids end up variously shot, knocked off the ship, and taken out by R2. If the missile had just hit him and exploded like any sane design would have had it do, Obi-Wan would've been dead. Even if Anakin's stunt in saving Obi-Wan was far-fetched and a very unlikely scenario, it would certainly still have been cheaper to pack an explosive warhead into the missile rather than a bunch of saboteur droids.
Han Solo pointed out that the lightsabers are completely useless in a fight compared to blasters. That's true unless the wielder is a Jedi.
Believe it or not, the titular character's armor was like this for a while in the first film. One montage shows Tony Stark repeatedly testing the armor and correcting various design flaws that crop up. Among these problems are the fact that the suit tends to freeze up when Tony flies too high into the sky. This serves as Foreshadowing for the final battle, when Tony—who has already experienced and solved the problem of his armor freezing—lures Obadiah Stane, whose armor is reverse-engineered from one of Tony's earlier models to that very same height.
In Iron Man 3, the Mark 42 armor. It's Tony's most advanced suit to date, but it never leaves an unfinished prototype stage, and its ability to deploy piece-by-piece and assemble on the wearer makes it alarmingly easy to break apart. The Assembly part was also clearly not well thought out, as one point Tony gets effectively punched in the jewels by his own codpiece.
Batman has the Batwing. Looks like another cool addition to Batman's arsenal; a modified stealth jet complete with Gatling guns, missiles and a price tag that had to be somewhere north of $2 billion back in 1989. Has an utterly god-awful targeting system (it's completely unable to hit a man-sized target under ideal conditions) and goes down in one shot from a pistol (which was itself a pretty silly piece of equipment: having a barrel nearly as long as an arm made it awfully hazardous to draw).
Batman Returns has Bruce's entrance to the Batcave: It involves reaching into a fish tank to open an iron maiden, which retracts it's spikes and dumps him into a slide that carries him to said cave. It gets him there slightly faster than his elderly butler who just takes the stairs.
How Bruce is able to acquire his gear in The Dark Knight Saga: The military developed incredible technology for one man to effectively wield — as Batman would illustrate — but were too costly to mass-produce, leaving Wayne Enterprises to stockpile the prototypes under Lucius Fox's watch at R&D. One example from Batman Begins is the advanced body armor that Bruce turned into the Batsuit. Reinforced joints, tough enough to stop a knife, and bullet-resistant, but:
Lucius Fox: Bean counters didn't think a soldier's life was worth 300 grand.
The Incredibles: One of the more well known lines from the movie: "NO CAPES!"
The Jackhammer Massacre; it's cool and certainly mangles well, but is shown to be heavy and awkward to wield, and is severely limited by its need for an extension cord (the killer is basically beaten when it's unplugged).
The Enforcement Droid (ED) 209 from RoboCop (1987). It's a badass-looking walking mech with machine guns for hands, and one of the most awesome-looking things in the movie. But it was rushed out and unfinished, leaving it with a lot of design flaws, including the inability to use stairs, the inability to right itself when it's fallen down, and a programming flaw that keeps it from realizing when a suspect has surrendered. ED-209's impracticality was what led to the creation of Robocop. ED-209's model designer envisioned OCP's engineers focusing on making the robot look good/intimidating before making it work well, "just like an American car". Based on some dialogue from Dick Jones, it seems this was partly intentional. The plan was to make millions selling a defective machine, then make even more millions charging customers for frequent repairs.
The Götterdämmerung in Iron Sky. The Moon Nazis' (It Makes Sense in Context) flagship is several orders of magnitude larger than any other ship in their arsenal. Its cannons (firing Depleted Phlebotinum Shells) are capable of tearing enormous chunks of the Moon with a single volley. It doesn't appear to have any other weapons to defend itself from smaller attackers (and its main gun's targetting system is too slow). The Bridge is exposed. To top it off, it's way too complex for the primitive Nazi computers to run. Luckily, a single smartphone can succeed where a room-sized ENIAC clone will fail. The Moon Nazis' goal is to conquer Earth, not render it uninhabitable. So why build a weapon that can do the latter but not the former instead of using those same resources to double the size of their fleet?
In Looper, which takes place in 2044, about 10% of the population are "TK", or telekinetic. Most of them can't do any more than move small objects with their hands, though. However, the future Big Bad, The Rainmaker has the power to do this on a large scale, so the trope is subverted.
The powered suits from G.I. Joe: The Rise of Cobra, as demonstrated in the Paris chase scene. They can't catch up with a vehicle that is weaving through heavy traffic. After the chase, they can't even properly catch up with two people on foot.
In Operation Lovebirds, Frede's pistol can fire both forwards and backwards. However, he has a difficult time telling which setting is which.
In Sergeant Bilkos Hover Tank, a tank that goes anywhere a hovercraft can, but one shot from its cannon causes it to recoil wildly.
The war rhino in 300 is certainly quite impressive, but it gets killed by a well thrown spear before it even has a chance to reach the Spartan front line. Furthermore the war elephants, which the Spartans manage to push off the cliff. note A scene maybe inspired by this◊ picture, concerning another war in Antiquity.
Emmet's plan for a double-decker couch in The Lego Movie. It's a cool idea, and lets six buddies hang out and watch the game. But if the guy on top centre wants to get down, how do they do it without climbing over the guys next to him? And do the people on the bottom couch get a clear view, or do they just watch three pairs of dangling legs? It's Played for Laughs, of course.
Into The Storm. The idea of turning ships into icebergs to disguise them sounds brillant at first, but then...
Ismay: Icebergs travelling in formation, sir? At a steady eight knots?
Winston: We'd have to work on the details..
Ismay: ...And with smoke coming out of a funnel?
Sanosuke's zanbato in Rurouni Kenshin. Sure, it looks cool, but it's also so big and cumbersome that all but the slowest of opponents have an easy time evading blows from it.