I was pretty psyched at around the 0:37 mark when Jonathan Crane showed up. Other than that, the animation is pretty cool, but as an intro, there's too much 'stuff' and not enough context. Don't get me wrong, I understand wanting to show off weapons and powers and all, but there's no reason to care about any of it.
Thing is, for me to enjoy a fight on it's own merits, without any story context, said fighting has to be balls to the wall incredible. The above video was neat, but it wasn't a "fighting for the sake of fighting is rad" experience, or at least not to me.
What would have made it better? For me, I knew none of the characters' backgrounds, I only knew the Scarecrow guy is named Fiddlesticks, but I still enjoyed seeing all these neat colourful characters come to life and fight, even if I didn't know them.
I'm pretty sure the Scarecrow guy's name is Scarecrow. At least according to the old DC Universe Handbooks. Anyway, so far as improving the video goes? I can't answer that in any objective way. It's not so much that I think it's bad rather it simply didn't do anything for me. If, however, it attracted someone unfamiliar with the series such as yourself, it has to be considered something of a success.
Purely subjectively, though? Voiceover, showing a couple of characters outside of combat, or even the briefest explanation of the setting would work wonders.