Broken Base: Some say it's one of the best episodes of the show. Others (including Matt Groening himself, which explains why his name isn't in the opening credits) say it's one of the worst because it's a crossover, Matt Groening promised The Simpsons would be an anti-sitcom filled with all the things that normal sitcoms wouldn't have (and, apparently, that includes spin-offs and crossovers), and most Simpsons fans at the time thought The Critic wasn't a good show.
Crosses the Line Twice: In Barney's film, we see him introducing himself at what seems to be an Alcoholics Anonymous meeting, but we zoom out and see Lisa informing him he's actually at a Girl Scouts meeting. To which Barney says "Is it, or is it that you girls can't admit you have a problem!?"
Family-Unfriendly Aesop: Homer is admonished for voting for the (admittedly lowbrow) movie he enjoys and when he ultimately does vote for Barney's film, Marge smiles with a declaration of "You voted for the right movie." That Homer changed his vote from one he enjoys to one his peers approve of is treated as absolutely a good thing. It is definitely possible that Homer legitimately changed his mind upon watching Pukeahontas but it didn't take much from the fact that Marge expected him to vote for the choice of which she approved.
"Funny Aneurysm" Moment: McBain's Take That at Woody Allen, "I'm a neurotic nerd who likes to sleep with little girls.", originally referencing Allen's marrying his adoptive daughter Soon-Yi, became more cringe-worthy in 2014 when her stepsister Dylan Farrow accused Allen of molesting her as a child.
Germans Love David Hasselhoff: The episode's a lot more popular outside of the U.S., since The Critic didn't get exported to that many countries (and wasn't promoted much in the ones it did get to). The whole crossover controversy therefore went over the heads of most international viewers, who tended to assume that Jay Sherman was either a real-life film critic, or a character created specifically for this episode.
Overshadowed by Controversy: Any attempt to discuss the episode tends to get bogged down in arguments as to the idea of a crossover with The Critic, to the extent where staff writer Ian Maxtone-Graham (who didn't start working on the show until the season after this episode was made) was excoriated by many fans for attempting to defended it as a good episode if you take it purely on its own merits.
Tear Jerker: Barney's film about his alcoholism ruining his life (except for the part where Barney mistakes a Girl Scout meeting for an Alcoholics Anonymous meeting), which makes the flashback of how Barney first got drunk (Homer gave him beer the night he was studying for his SATs — and what's worse, Barney was a Harvard-bound genius in his teens) harder to laugh at in hindsight.
After winning, Barney promises to go on the straight and narrow, at which it's announced he also won a tanker full of Duff beer.
Barney:JUST HOOK IT TO MY VEINS!(truck driver obliges with an IV)