Does it have to be a stupid automotive design? Because I'd like to nominate the Mercruiser 3.7 liter 4 cyl (the "470") engine from the marine world. It was (and is) still being used to some degree in the automotive world by some diehard enthusiasts, so I'l throw it out there.
Ford 460 V8 driver side cast iron head, mounted to a home baked Mercruiser open deck aluminum block, fitted with a woefully inadequate 3 inch heat exchanger to keep it all cool, in an application where engines are routinely thrashed at or near full throttle a big chunk of their life. Can you say "blown head gasket"? This engine would eat head gaskets at a temperature that many automotive engines idle at in the dead of winter on the north pole.
To add insult to injury, the water pump was similar to the latest Ford abomination, and was nothing more than an impeller bolted to the front of the camshaft, separating the cooling water from the crankcse with two small seals the size of your pinky. Why? Because no belts required, thats why. There was a weep hole between the seals, but that void was filled from the factory with grease, and over time that grease would harden and plug up the hole, so when the water seal went bad, the antifreeze would plow past the second (oil) seal and dump into the crank, taking out the rod and main bearings, the cam, and the now lack of water overheated the engine and your wallet in the process, because now your cam, bearings, crank, and rods are wiped out, your head gasket is shot, and you may need to machine the block flat again as well depending how hot it got.
To add further insult to an already expensive injury, the alternator was nothing more than thin permanent magnets glued to the inside of the crank vibration damper, which spun around the block mounted copper wire coil, producing nonstop voltage proportionate to the rpm. Why? No belts (again), thats why. Similar to a lot of outboards, just woefully worse. The current was routed to the voltage regulator bolted to the side of the block, which was a water cooled potted carbon resistor that burned off unneeded amperage as necessary. These things burned up quicker than the Hindenburg (and your battery as well), on a regular basis to the tune of $200+, and thats in 1980's dollars. Most people just clipped the wires and spent an afternoon in a junkyard pulling every alternator bracket they can find, and adapting a GM 10Si marinized one-wire alternator, and calling it a day (the crank damper was grooved for a belt, for applications that needed one to run the power steering pump). Or spending $400 on an aftermarket prefab kit that did the same thing.
Later models had a 4 inch heat exchanger and a better head gasket, which helped greatly to keep it cool and mitigate the head gasket issue, and the aftermarket kept the alternator issue at bay, but the water pump remained a weak point until the bitter end.
In the hands of the right person, a 'car guy' or someone who was hyper-diligent on maintenance, they were a lightweight, fuel sipping torquey monster that with minimal tweaking and a quadrajet in place of the 2 bbl were pumping well north of 200 HP, which was pretty impressive for an 80's era four cylinder. It pulled my little boat like a beast. But the horrible alternator, equally horrible water pump, and fragile head gasket situation sealed their doom and Mercruiser mercifully pulled the plug on this animal after about 10 years or so and let the simple, trusty and durable GM 4.3 V6 fill the void. Want a cheap boat? Find one for sale that has a "Mercruiser 3.7" or "Mercruiser 470" engine. The seller will probably give it to you, throw a few hundreds at you in the process, and tap dance happily back to his house as you pull away with it.
A number of these engines found their way into sprint cars, Model A's, kit cars and various other car projects, because like I said in the right hands they can be a lot of power in a small package, they are easily modified, and parts are still pretty easy to get, but you have to treat them with kid gloves unless you really like rebuilding engines. As far as stupid designs, this one is a collection of them mixed into one big absolute turd of an engine.
Wasnt there a Ford or GM truck back in the 60's or 70's that ran the windshield wipers off a hydraulic motor powered by the power steering pump? Cant remember where I saw that or what make it was, but that would be my first runner up.