Short answers, pulled from the story.
Continuity in fiction is the consistency of characteristics of people, plot, objects, and places as an audience experiences them over time. It matters because errors break the audience's suspension of disbelief, and in film and television they are difficult to fix after filming ends.
A Homeric nod is a continuity error in a work of fiction. The term comes from a phrase coined by the Roman poet Horace in his Ars Poetica, referring to the continuity inconsistencies found in Homer's Iliad, such as the character Pylaimenes being killed in combat and then reappearing alive later in the same poem.
Soap Opera Rapid Aging Syndrome, or SORAS, is the practice of accelerating a television character's age far beyond what the series timeline would support, usually coinciding with a recast. An example is the BBC series Merlin, where Mordred is a young child in Season 4 but appears as a young man in his late teens in Season 5, while other characters aged only three years.
A script supervisor monitors actors and sets throughout filming, gathering paperwork, photographs, and documentation that record details both within scenes and technical production details such as camera positioning and equipment settings. This information allows the crew to match related shots even when filming is split across months on different sets and locations.
A retcon is a retroactive change to established continuity in a story. It differs from a full reboot in that it preserves the larger narrative structure while introducing a new explanation for an earlier inconsistency. The character Frasier Crane's contradictory family history across Cheers and the Frasier spin-off was resolved with a retcon explaining that Frasier had lied about his father.
Fanwanking refers to unofficial fan-generated explanations invented to smooth over continuity errors or inconsistencies in a franchise. The term was originally coined by author Craig Hinton to describe the excessive use of continuity references, and has since broadened to cover any unofficial explanations fans create for narrative contradictions.