OK, I wish I had thought of these, but here are several very funny star trek jokes from therealtalkingfish.tripod.com
Please post your own observations of "Things that dont happen in Star Trek"
Things that don't happen in Star Trek: --The Enterprise runs into a mysterious energy field of a type that it has encountered several times before.
--The Enterprise goes to check up on a remote outpost of scientists, who are all perfectly all right.
--The Enterprise comes across a Garden-of-Eden-like planet called Paradise, where everyone is happy all the time. However, everything is soon revealed to be exactly as it seems.
--The crew of the Enterprise are struck by a strange alien plague, for which the cure is found in the well-stocked sick-bay.
--A power surge on the Bridge is rapidly and correctly diagnosed as a faulty capacitor by the highly-trained and competent engineering staff.
--A power surge on the Bridge is fails to electrocute the user of a computer panel, due to a highly sophisticated 24th century surge protection feature called a 'fuse'.
--The Enterprise ferries an alien VIP from one place to another without serious incident.
--The Enterprise is captured by a vastly superior alien intelligence which does not put them on trial.
--The Enterprise separates as soon as there is any danger.
--The Enterprise is captured by a vastly inferior alien intelligence which they easily pacify by offering it some sweeties.
--The Enterprise is involved in a bizarre time-warp phenomenon, which is in some way unconnected with the 20th century. [note: this one actually happens in First Contact, since that was the 21st century. Also visited was the nineteenth century, when Mark Twain found himself beamed to the Enterprise, and was asked to refrain from smoking.]
--Somebody takes out a shuttle and it doesn't explode or crash.
--A major Starfleet emergency breaks out near the Enterprise, but fortunately some other ships in the area are able to deal with it to everyone's satisfaction.
--The shields on the Enterprise stay up during a battle.
--The Enterprise visits the Klingon Home World on a bright, sunny, day.
--An attempt at undermining the Klingon-Federation alliance is discovered without anyone noting that such an attempt, if successful, "would represent a fundamental shift of power throughout the quadrant."
--A major character spends the entire episode in the Holodeck without a single malfunction trapping him/her there.
--Picard walks up to the replicator and says, "Coke on ice."
--Kirk falls in love with a woman who, unfortunately, can't take the time off from her career. She leaves him in the end.
--Scotty assures the captain that repairs will be possible, but they turn out to be against the laws of physics.
--A well-equipped, large landing party is well-equipped with security officers, and none of them die.
--Mr. Spock is among the victims of a strange alien threat, but because of his Vulcan metabolism, he succumbs more quickly.
--The unique interplay of abilities and personality traits of the command crew make them unable to solve a crisis.
--Mr. Worf demonstrates the Klingon Flower Ritual.
--Mr. Data links his brain directly to the ship's computer, reads and sends data, and then routinely breaks the connection without mishap.
--I find out what happened to Mr. Worf's (quite understandable) feelings for Counselor Troi.
--A member of the crew of the original series makes an appearance without maudlin references to and jokes from the original series and the films.