The categories are broken down according to which holds precedence over the show, because some episodes are built around multiple failures but one is the key to everything.
Misguided/Misunderstood Science and Research (10 entries) When Starfleet doesn't bother paying someone to run a few simulations or run a few extra tests and just puts it out in the field.
- TOS: The Ultimate Computer
- TNG: Where No One Has Gone Before
- TNG: Datalore
- TNG: We'll Always Have Paris
- TNG: Unnatural Selection
- TNG: Remember Me
- TNG: The Nth Degree
- TNG: Genesis
- VOY: Threshold*
- VOY: Spirit Folk
- TOS: The Enemy Within
- TOS: Mirror, Mirror
- TNG: Hollow Pursuits
- TNG: Data's Day
- TNG: Realm of Fear
- TNG: Rascals
- TNG: Second Chances
- VOY: Non Sequitur
- VOY: Tuvix
- VOY: Macrocosm
- TNG: The Big Goodbye
- TNG: Elementary Dear Data
- TNG: Who Watches the Watchers
- TNG: A Fistful of Datas
- TNG: Ship in a Bottle
- VOY: Alter Ego
- VOY: Worst Case Scenario
- VOY: Latent Image
- VOY: Bride of Chaotica!
- VOY: Flesh and Blood
- TNG: 11001001
- TNG: Contagion
- TNG: Peak Performance
- TNG: Evolution
- TNG: Conundrum
- TNG: Starship Mine
- VOY: Heroes and Demons
- VOY: Projections
- TNG: The Child
- TNG: Disaster
- TNG: Relics
- VOY: Twisted
- VOY: Dreadlock
- VOY: The Swarm
- VOY: Threshold
Also a breakdown of the engineering failures of the movies for your enjoyment.
Motion Picture
- Transporter Accident (When the two crewmen died during transport)
- Technobabble Failure (Pressed into service without finishing out the ship)
- Failure for No Real Reason (The Mutara Nebula)
- Failure of Security/Safeguards (Spacedock doors opened remotely, Scotty sabotages the Excelsior)
- Technobabble Failure (When Genesis just blows up because it's unstable)
- Ungodly Influence (The Whale Probe)
- Failure of Security/Safeguards (Too many to list)
- Technobabble Failure (Too many to list)
- Ungodly Influence (God wanted a Star Trek V, but the Devil picked the director)
- Failure of Security/Safeguards (Unaccounted for torpedoes, Unregistered transporter use)
- Technobabble Failure (Warp Core Breech)
- Failure of Security/Safeguards (Enterprise B only ship in range with no crew, Dr. Soren's secret lair)
- Transporter Failure (Secret transmitter in Geordi's visor)
- Technobabble Failure (Borg Adaptability, No access to shuttlepods, loss of power, no internal sensors)
- Failure of Security/Safeguards (Beaming down to unsecure location without sensors)
- Holodeck Failure (Fake guns kill real people)
- Misunderstood Science (Sona and their obsession with the metaphasic radiation, exploding gas in space)
- Failure of Security/Safeguards (Holoship's controls hacked, lack of Starfleet presence, phasers carried by observers, ejecting warp core during battle)
- Holodeck Failure (Imperfect holomatrix on holoship)
- Failure of Security/Safeguards (B4 brought aboard and assembled after Lore incident, Violent interaction with planet's inhabitants, Flying through nebula instead of going around)
- Technobabble Failure (New containment field around warp core suddenly fails, forcefields take too long sealing breech)
- Transporter Failure (Sensors don't work to beam Data over, but can instantly lock on to emergency beacon)