TMP has a HUGE plot hole. A near-god-like living machine, which can digitize entire worlds and star systems and created a near-perfect android duplicate of Illia, never thought to wipe the muck off it's name plate?
Wrath of Khan's entire "two dimensional thinking" thing made zero sense, especially if Khan is the genius he's repeatedly said to be. There are also problems with Ceti Alpha VI somehow blowing up, the Reliant somehow not noticing such a massive change in the solar system (did nobody count the planets?). And why didn't Khan just beam Kirk up for torture and execution when he took the entirely magical Genesis device? Which somehow despite being designed to convert the surface of a barren world into a living planet, managed to build an entire world (and star!) out of a nebula?
Search For Spock is pure Vulcan hocus pocus, with not an ounce of realism or science fiction. Spock's ageing just happening to sync up with them arriving and leaving... uh huh. Also, Excelsior spluttering to a halt totally ignoring the laws of physics.
Bored now. But there are more. Lots more. And people like to pretend JJ Abrams' Treks invented plot holes. LOL!
(and I love the old movies too!)