This is a pre-9/11 world, so the world "terrorism" isn't a magic word that can be applied to everything. Vertigo participated in a supervillain attack.
Also, Vertigo didn't kill anybody himself, so he'd be charged with, what ... aiding the Joker, and maybe assault if the Team pressed charges? I guess they could push for attempted murder on the "attacking the Team" thing.
Oddly enough, in a sane world, this would actually be the 9/11 equivalent, at the very least. The attacks were wide spread enough that it would be difficult to find someone with access to television who didn't know, personally, someone who was in danger of dying to this attack.
As for what they could be charged with? Even if they somehow didn't kill anyone, they still hit multiple cities with attacks that could have easily killed large portions of the population of those cities.
And no, 'We knew the law enforcement people would stop it' doesn't make it not attempted murder.
Moreover, they went on an international broadcast to tell everyone about it.
And no, recording a crime and publishing it doesn't make it not attempted murder either.
Even without the various conspiracy laws (designed to make it possible to prosecute organized crime, which this pretty clearly would be), accessory to attempted murder alone can carry a life sentence in many places. Most of which these attacks hit. With just London and
New York Metropolis they'd be looking at over ten million counts of that.
Even if they managed to beat the murder charges, somehow, this much property damage doesn't just carry a fine.
As far as diplomatic immunity goes,
here's the wikipedia article on it, and the section on people who actually committed serious crimes, like a piddling two or three counts of assault or murder. While deportation (Persona non grata) does happen, and diplomats can get away with drug smuggling and parking violations, in more serious cases the immunity is often waved by the country of origin.
When it isn't, well, sometimes nothing comes of it, but a few murders involving embassies have contributed to outright conflict. The shooting of a British police officer from the inside of the Libyan embassy that led to a breakdown in relations, and later contributed to Thatcher's support of Reagan's bombing of Libya, being the one that most stands out in my mind.
And this is a little more than 'just a few murders.'
