I really hate to say this but...

The schmaltz with Oliver and Felicity was groan-worthy, as usual.

I have mixed feelings about Batwoman; they just sort of went with the same stock depiction of a grumpy vigilante that they've applied to a thousand Batman movies and has served as the premise for Arrow for seven seasons.  I'm mostly disappointed that this is Earth 1 Batwoman after all.  When speculation abound as to how Batwoman, let alone Batman would fit into any of this, the most promising explanation was that Batwoman could be from an alternate Earth or "elseworld" that would allow a more open interpretation that wouldn't undermine the potential appearance of an active Batman on Earth 1.  So naturally they went the other way; and pretty much exactly like they did with the failed Birds of Prey series way back when, their only explanation for the absence of Batman is to have him leave Gotham, which by and large is completely antithetical to the character.  The only saving grace was the debate over whether or not Batman was real or myth, which is how the character should be portrayed in order to be effective and to properly conceal Bruce's identity.  Yet the way the way they included Batwoman felt like more of the same; there's no subtlety and she drops coy hints, not just about her own identity, but seemingly Bruce's too.  I want to give the benefit of the doubt that the only reason Kara put two and two together that Kate was Batwoman was because she already knew the identity of Batman on her Earth, but between her comment about using her x-ray vision and the hints dropped by Kate, it seems more likely that Kate is pretty much making the same mistakes Oliver, Barry and Kara all have made; and that more people are able to figure out her identity than should be able to. 
More time could have been spent defining her character, especially if this is to serve as a backdoor pilot for a potential series (and maybe there's more of her in Part 3).

I was also very disappointed with how little they used Earth 90's Flash, seeing how much they touted him in the promotion of the crossover; and that he was used in the teaser last week leading up to this.  He barely shows up long enough to tell them about the book, and then immediately gets winked out of existence.  Again, maybe he'll reappear for a good portion of Part 3, but I'm not holding my breath.

One last up side, I like Earth 90's Flash mentioning John "not wearing his ring" - which I took to implicate that on his Earth, John's doppelganger is a Green Lantern; possibly John Stewart.