I've just rewatched the three parts of the crossover this afternoon (the Supergirl scenes having been repeated in The Flash), and I enjoyed it. There were some things that I felt could have been done though I accept time and/or the availability of certain cast members would have made these things difficult or impossible.
Firstly I thought it might have tied Supergirl into the crossover if the WMD that her birth father had been working on on Krypton - Medusa - had been designed as a result of the Dominators' invasion of Krypton. Secondly although she seemed to get over her angst-ridden feelings about her father and his role in all that, perhaps Kara could have benefitted from hearing Oliver talk about his father's sacrifice as well as Barry.
It might also have been interesting if Alex had not hooked-up with Maggie Sawyer in the Supergirl episode (but she did in a future one) but instead had been at Kara's apartment when Barry & Cisco appeared and accompanied her back to Earth-1 and had had a chance to interact (and that's not a euphemism) with Sarah Lance, perhaps got her advice.
Speaking of Sarah, given that she just happened to be in the 'temporal neighbourhood' perhaps Thea could have mentioned to her that her father had fallen off the wagon and she could have gone and seen him about his drinking.
At the end when Kara is talking to Oliver & Barry about how it's only her and Superman on Earth-38 she could have said:
"Oh, and there's this guy in Gotham, who from what my Cousin says is a lot like you Oliver. Only his schtick is bats rather than bows and arrows." Given the Gotham reference in the Supergirl season opener and the reference to 'that other other city where they wear masks' in season one, I thought that could be awesome.
Then of course there's Lynda Carter playing the new Earth-1 president (by the way what happened to Obama is he another Flashpoint victim?).
As for future crossovers, I don't know where they're going with the Guardian thing on Supergirl but assuming Kara discovers Jimmy is the Guardian perhaps an episode (it might only need to be a cameo) in which Oliver is brought to Earth-38 to lecture/mentor Jimmy. I'd also like to see Superman hope universes and appear in Earth-1. Speaking of Superman I thought of how they could do a spin-off show. instead of it being on Earth-38, it could be on Earth-1 with it being that world's Superman played by Tyler Hoechlin. The Earth-1 Clark has not made his debut and is keeping is existence secret. Perhaps the events of the crossover are the catalyst for his coming out to the world. For the rest of their seasons you could have The Flash, Arrow and DC's Legends seed their episodes with references to Superman such as talking about Metropolis, Lex Luthor, The Daily Planet etc. Thus you could have a show that begins with the beginning of Superman's career and since Superman/girl age more slowly, he'd still be young and dynamic. Anyway those are just a few thoughts of mine. If these have come up in the existing threads for the existing shows I can only say I've been avoiding those threads as they're spoilery and we're a couple of weeks behind you with the episodes.
PS I loved Ray's comment at the end that Kara reminds him of his cousin.