I assume you don't count the Challenger and Columbia disastors, otherwise those win. Assuming you don't I can't decide which one as they had different types of problems but here are some troubled missions:
STS-93:It was scrubbed three times before launch. Then it
launched without 897 lb of LOX. Then, the wiring failed and caused
problems with a bunch of sensors. Finally, there was a deactivated
LOX post in the main injector. Of course, the biggest of all was that, during ingnition, a gold pin hit the nozzle extension, causing a nozzle leak. Due to a bunch of luck, disaster was averted. There are more, but those were the
STS-26: The flight after the Challenger disaster. It was scrubbed once before launch. A couple of problems occured. First, the FES (Flash Evaporator System) iced up and shut down leaving the crew in a shuttle with temperatures of around 87°F (31°C) until day 4 of the mission. Second, a Ku-band antenna deployed on day 2 but failed to respond. Gradual improvement.
STS-27:During the ascent, it appears that a piece of foam hit the shuttle, like in the Columbia disaster. The crew believed it to be unsurvivable. Luckily for them, the tiles that they hit covered something else that was steel, and therefore it didn't burn up on reentry. Lucky break. Gradual worsening.
STS-28:1 launch delay. First, a pyro initair circuit had an issue and failed. Then, an Exhaust Temp had an issue. Next, a regulator pressure dropped. Also, some recorders had issues, as did a camera which couldn't focus. Additionally, measuerer fuel was malfunctioning, as was the pitch and yaw actuators. The TPS (Thermal Protection System) also sustained some damage, although that is common. Then, a fuel cell's sensor failed. Also, the side hatch wasn't working as was very hard for the crew to operate. Finally, an airlock pin did not latch. Improvement, but a bunch of annoying minor issues.
Fortunately, STS-29 did not have any notable issues (about time). So, these are what I would call some of the 3 biggest cursed launches of the shuttle program.