Continuing a long-standing pattern regarding my preferences between non-cover Waynes and Wayne-ish personas vs Bat-personas, I think Kathy Kane is about 17% more badass than Batwoman, which isn't at all a low bar.
Also, (1), I'm convinced the writers read the World's Finest Elseworld (which would be an appropriate reference at many levels), and, (2), a couple of scenes were less openings-to-fanfic than first pages of.
By and large, adorable.
Yes, the ethics of everybody not going back to Earth-X to help are rather awful (fixing the timeline (they broke) might get the Legends off the hook, but there's nothing Kara, Barry, or Oliver are doing that has a higher priority than that), but that's the elephant in the room of all episodic media with superpowered characters.
Not that it would be that hard. Doing the crossover right before the series hiatus, you can have the characters spend those few months off-screen fighting on Earth-X. Lots of things can happen there to refer back to later if you need plot grist, important good gets done, and it reinforces the *scale* of what they can and do.
(That said, I acknowledge that Earth-X people might want neither Kara nor Oliver on their Earth; regardless of the good they can do, it'd, well, it'd be a mess. But Barry could certainly spend time there every now and then; plenty of uses for an speedster in a war, even one that won't kill.)
(Although Oliver could, in theory, try to pull a Prisoner of Zenda, and if not change things structurally, at least cause as much havoc as possible. The perhaps bleak and certainly psychologically harrowing long fanfic doesn't write itself, yet it whispers from behind your ear about how much good you could do with all that power... Not that I think Felicity would let him; that'd be a great way to break them up. But maybe she wouldn't let him do nothing, either.)
(In short: once you have well-meaning superheroes with access to a Nazi Earth, pretty much the only non-viable plot option is to have them not go there.)
But I digressed into a complaint; I enjoyed the event quite a bit, less because of the pace and plotting — as choppy and by the numbers as all such events are — than because of the small character moments. The Supergirl-Green Arrow-Flash ("Dorky Cinnamon Roll Who Could Level Your City," "Grumpy Cynic With The Soul of a Puppy", and "Dorky Cinnamon Roll Who's Actually 100% A Dorky Cinnamon Roll") TV Trinity works very well, mostly because they balance their most problematic traits (e.g., it's almost impossible for Oliver to over-brood around Barry).