Big-Lipped Alligator Moment: The part where Rincewind accidentally teleports himself and Twoflower onto an airplane in our world and ends up thinking that he is Dr. Rjinswand, (33, a bachelor, born in Sweden, raised in New Jersey, and a specialist in the breakaway oxidation phenomena of certain nuclear reactors [a fancy way of saying that they're uncontrollably on fire])... only for the Luggage to interrupt the whole scene.
Becomes Fridge Brilliance when you realize that it's all an extended pun: They were transported to another plane.
Also an Early-Bird Cameo for Roundworld, once The Science of Discworld makes our world a canon part of the Verse's reality.
Harsher in Hindsight: The plane being hijacked by a swarthy, bearded man. At the time, airplane hijackings were most often done by escaping criminals trying to get to a country they could seek asylum in — Cuba was particularly popular for those with Communist sympathies or mistaken belief that the country would harbour people who commit crimes in America. The act didn't become associated with Muslim extremists until the late '80s.
Hilarious in Hindsight: Rincewind muses on how there are too many heroes in Ankh-Morpork, and how the notable questing-grounds are so busy during high season that they plan to introduce a rota. A scene familiar to anyone who ever played a regular MMORPG, all of which came out well after this book was published (with the exception of certain MUD games).
Plus, the troll encounter plays out exactly like a random encounter in a console RPG.
Moral Event Horizon: Galder Weatherwax trying to outright kill his former student via magical arrow in the film. I mean, he had to take the spell back by force but that is harsh.
Out-of-Character Moment: It's done to establish the fact that no matter how close he is to certain death, he will always be saved by something at the last minute, but Rincewind's brief Driven to Suicide moment in the two-part film seems odd for those with his familiar tenacity and desire to live. Preferably in complete boredom.
Special Effects Failure: In the two-part film from SkyOne, please pay no attention to Cohen's clearly visible teeth.
Though Eric Idle is only four years younger than David Jason, and still would have been twice Rincewind's age from the books at the time of filming, so that wouldn't have resolved the issue. Casting someone in their thirties with no prior connection to Discworld adaptations probably wouldn't have gone down well with fans of the game either, to be fair.
There was also some displeasure over the casting of American actor Sean Astin as Twoflower, which was viewed by some as an unnecessary attempt to attract more American viewers at the expense of some of the original book's very British-y humour, and by others as whitewashing, since the books had firmly established that Twoflower is the Disc's equivalent of Japanese. However, Terry Pratchett defended the decision by pointing out that Twoflower was a blend of Japanese, American, and British tourist stereotypes in his first couple of appearances. And, since every Sky1Discworld adaptation has re-cast every character anyway, presumably if Interesting Times does get made they'll cast actors of Japanese/Chinese descent as Agateans when it becomes relevant to the plot.
Woolseyism: In the Swedish translation, Dr. Rjinswand is Dutch, since Rjinswand doesn't actually sound Swedish.