Author's Saving Throw: Jason and Medea are very much the Designated Hero in the original myth and film. The 2000 miniseries goes out of its way to make Jason more unambiguously heroic - being ordered to get the Fleece to save his mother's life. Medea likewise gets shown to grieve for the deaths of her father and brother.
Which film is better. Fans of the Harryhausen film defend it quite passionately, though some mistake the 2000 film for a remake when it's really just a Truer to the Text adaptation of the original myth.
The happy ending in the Hallmark film. Some despise it since this one is explicitly more faithful to the myth, and it contradicts the Downer Ending. Others feel it fits the tone of the story, especially since the Harryhausen film cuts off before the return journey to Pelias.
Including Atalanta in the 2000 film. Some invoke They Changed It, Now It Sucks and complain about political correctness (especially with the Affirmative Action Girl being involved in some kind of love triangle with Jason). Others are fine with it, since some myths do say that Jason included Atalanta on the voyage.
Big Lipped Alligator Moment: The dance scene in the Harryhausen film. In the Hallmark film, the scene where Zeus tempts Medea which is never mentioned again.
Complete Monster: In the 2000 Hallmark Made-for-TV Movie, Pelias, like his mythological counterpart, is the brother of King Aeson of Iolcus and an uncle of the titular protagonist, but is much more evil than in the myth or in the 1963 film. He and his soldiers invade Iolcus and terrorize civillians. In his Establishing Character Moment, he gives a hug to his brother only to stab him with the knife saying; "My destiny is to rule!" He attempts to murder the baby Jason, only for the latter to be saved by a bodyguard. Couple years later, Pelias sends an adult Jason on a dangerous mission to find the Golden Fleece, hoping that Jason never succeeds, and threatens to kill Jason's mom whom he earlier forced to marry him. Near the end of the film, when his son, Acastus, brings Pelias the Golden Fleece, Pelias fakes gratitude and murders his own son, taking the Golden Fleece. Seconds later he holds Medea hostage. In his final act of malice, Pelias lies to Jason that he has been overcome with madness by the Fleece while giving him a hug, but secretly he was just trying to kill Jason in the same way he killed King Aeson earlier.
Designated Hero: Jason, full stop. His goal to take back his kingdom may be admirable (though we don't know for sure if his father Aristo wasn't, say, a brutal tyrant), but it's hard not to notice his blatant indifference to the loss of crewmen over the course of his journey or his plans to filch the Golden Fleece out of Colchis.
Averted in the Hallmark film where he must find the Fleece or else his mother will be killed.
Hera is one of the most memorable things about both films. It helps that in the first Honor Blackman absolutely steals the show, and overall it's one of the rare myths in which Hera is heroic (rather than the Evil Matriarch she normally is).
Acastus in a sense, given how both myths apply Adaptational Villainy - leaving viewers feeling sorry for him. He's also sympathetic in both versions, since the Harryhausen film has Jason attempting to usurp the throne from him. And in the 2000 version he's a "Well Done, Son!" Guy.
Hilarious in Hindsight: Brian Thompson plays Demigod Hercules in the Hallmark film. A few years later he would get bumped up and play Cronus in Charmed.
Ho Yay: Hylas and Hercules sure do pair up quick. Hylas essentially dies trying to pick up after his thoughtless boyfriend and, afterwards, Hercules quits the quest to retrieve his body.
Narm: A good chunk of the Harryhausen film due to Todd Armstrong's awful acting, the fight with Acastus in particular. The harpy scene also fails to be anyway intimidating.
The last few scenes in the Hallmark one are made comical by the fact that Pelias is actually wearing the Fleece and looks quite ridiculous.
The fight with the Skeletons starts out ok, as they silently, slowly march forward...before letting out a high-pitched "war cry" that sounds like a pack of angry schoolgirls. The scene continues on and is rightfully lauded, but for that one moment...
Nightmare Fuel: Everything with Talos in the Harryhausen film, from the moment he wakes up and starts chasing the Argonauts to his death scene, where he grabs his throat and starts making noises like screeching metal.
One-Scene Wonder: Honor Blackman steals the show in the Harryhausen film, playing Hera. Olivia Williams steals the show in the Hallmark film, coincidentally also playing Hera.
Visual Effects of Awesome: Every monster in the movie, but the crowning moment is undoubtedly the fighting skeletons scene. That 3 minute scene took Ray Harryhausen 4 months of solid work! The Talos scene also holds up reasonably well over the years.