Regarding Jay's appearance on The Simpsons..Jay was a guest star on The Simpsons. Jay exists in The Simpsons universe, hence why no else one from The Critic appeared. Jay's not a Butt-Monkey in his appearance which was probably made after he met Alice or is a case of inverted Adam Westing.
- Alternatively, Jay's appearance in A Star is Burns isn't canon to The Critic (probably All Just a Dream for him), but his cameos in Hurricane Neddy and The Ziff Who Came to Dinner were. When his show got canceled, Jay suffered a breakdown and wound up in that same hospital seen in Neddy. Once he got better, he went on to do his web show, then fell on hard times when it too got cancelled. He probably became alcoholic, which is why he shows up at Moe's in Ziff.
- Possible reasons that we don't see the rest of the cast with Jay is either his breakdown unintentionally scared them off (probably the case with Marty and Margot), they gave up on him and moved on (probably with Jay's ex-wife), or they passed away (probably with Duke, Doris, & Jay's parents, if they didn't abandon him beforehand). Vlada's still got a restaurant to run, so whether he cares about Jay as a friend is up to you.
- Jay's breakdown might have been terrifying enough for Alice to fear for Penny's safety, and so she left Jay and NYC and never saw him again, which is why Jennifer is Jay's love interest in the web show. Jennifer stuck around until the show got cancelled, then she dumped him and moved on.
- Another hypothesis is, Jay wasn't a Butt-Monkey in the episode because the "actual" Jay (or more likely, Duke) demanded the writers portray him more sympathetically. Of course, that pissed off Matt Groening quite a bit - meaning, in the universe of The Critic, Matt hates that episode not because it's a crossover, but because they sold out to a celebrity...like they would often do on the coming years.
- Or, he's still a Butt-Monkey in New York, but in a place like Springfield he's still a cut above most Springfieldians; note how much Homer felt threatened by Jay, and how Jay was able to impress everyone and even charm Patty and Selma (until he told them MacGyver is gay...).
Jay's boss Duke Phillips is a Depraved BisexualHe's the one who has a crush on Jay and makes jokes about Jay to cover up his insecurity. He's from the South where homosexuality isn't as tolerated.
- Him giving Jay a kiss and calling Jay his "Special little guy" was him using the situation and his reputation for being nice to those he's about to punish to get in a moment of genuine affection without appearing too far out of character.
Doris really is Jay's Mother.The DNA Test results were switched or of poor quality.
Every movie in Hollywood since 1994 has taken a page from the show.Many jokes on the show came true in real life. The show had a bigger cult following than we know and any bad movie that's come out or sequel they predicted was due to this show.
The people who made the Saturday Night Live 40th Anniversary Special borrowed from this show.In "Dukerella", Jay tries to get Hollywood to make the movie "Dr. Strangelovitz", but the producers think he died. 20 years later, the SNL 40 special has two jokes in it where they list Jon Lovitz as deceased, only to immediately show him in the audience, confused as why people think he's gone.
Duke knows Noah Webster is dead.A famous scene in this show involves Duke making the word "quyzbuk", and when Marty calls him out for it, phoning Noah Webster to bribe him to make it a word, supposedly ignoring Noah being dead for who-knows-long. However, it's entirely likely that Duke knows this, and was just playing so that way Marty (who's young and gullible in this scene) will shut up about it.