You are so swift with postings, that I didn't have a chance to amend one thing I put in. The Batman movie franchise can be linked to one of the Tube Worlds. Follow my logic (and I know, it can be a long, strange trip)...
The Batman movies from Tim Burton, et al were evoked in a few commercials, putting them onto some earth. There was both a Diet Coke ad and an ad for On*Star featuring Michael Gough's Alfred, so I assume that means he and the Batman are part of a BlipVert world or possibly Prime-Time Delayed. The Batman in those On*Star ads is clearly meant to be the Tim Burton-era Dark Knight, with the Batmobile, architecture of Gotham, etc. all matching. That Batman (the stuntman in the Batsuit appearing in the commercials) played Batman in a flashback on Birds of Prey.
As I've written you before, BoP makes a great link to the animated WB shows, with Mark Hamill providing the Joker's voice in a flashback on the live action show and having been the voice of the Clown Prince of Crime throughout the WB's run of shows, which I assume are part of the Prime-Time Delayed.
Ok, that's enough for now!
Pretty much I agree with all of Hugh's ideas, although I'm tempted to dump all of the animated Batmans into the Tooniverse, that alternate realm where animated characters hold sway. And the splainin for the difference between the Batman of 'Super-Friends' and the Dark Knight of the WB canon?
Who knows? Still another alternate to the Tooniverse? (The Twoniverse?) Perhaps the next generation of sons picking up the mantles of their fathers in both the cases of Batman and Robin? Or perhaps a self-adjusting time loop? (Sorry, I've been delving into Douglas Adams again.....)
It's going to take some thunkin' on my part. I don't want to just toss out a theory without working out all the possible Zonks it may create. When it comes to the contradictions to be found in the TV Universe, I'll leave that to the experts - the writers, producers, directors, and actors!