I tried going through and analyzing the trailer myself in a post on reddit. It seems most of you all have picked up on what I caught as well, but I'll post it here for reference's sake:
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I'm far too caught up in Smash hype now to do anything but think about these videos, so I decided to look at the Mewtwo video more closely and catch any new information they offered. Here's everything I was able to pick up on throughout the trailer.
You can follow along by watching the video:
https://www.youtube.com/watch?v=WvbwZYV7W0Q
0:17 The pose Mewtwo goes into here seems to be part of his idle animation from Melee
0:19 This appears to be a new taunt, followed by Teleport. Notice the effect that starts the Teleport off and the sound it makes.
0:21 Mewtwo's Jab from Melee returns, but now with an added finisher
0:23 Mewtwo's Dash attack returns as well, looking a bit more nicely animated
0:24 Mewtwo disappears, but due to lacking any sort of starting or ending effect, I reckon this is his air dodge ala Palutena and Rosalina. It might look like he double jumps into what seems to be his nair, but he actually lands. Previous jump height status unknown. Nair seems to have some nasty end lag to it.
0:28 Mewtwo's old hanging on the edge animation is back. Down Air is back and it's QUICK! This almost looks Brawl Falco Dair quick, though I might be a little over optimistic.
0:30 Mewtwo's Old Up Throw, Back Air, and previous ridiculous jump height are all back
0:34 Old Down Smash is back. No visual que that it hits behind mewtwo, though
if this darkness effect is the moves's range, that's a much welcomed buff.
0:35 Shadow Ball still whirls and has a new fully charged sound effect. You can hear Mewtwo's voice as he throws the attack, so it looks like his Melee voice is back
0:36 Teleport is back with a new sound effect. Doesn't seem to have a hitbox
0:38 Confusion is back and is either very quick now or jump cancellable. I'm not sure what its previous capacity for interrupting attacks use to be but it stocks Charizards recovery and sends him into a tumble animation. IIRC, you can't tech a tumble, so this could lead to some jab lock style follow ups if you catch your opponent in midair
0:39 Disable is back and makes Mewtwo's eyes green for a second (ruined forever!)
0:42 Mewtwo's Confusion shows off its priority again stopping Greninja's counter. It does seem to just be much faster now since he can swipe with a beamsword right after
0:44 Old F-throw is back, Shadow Balls included.
0:46 This costume seems to be based off of the Shadow Lugia from Pokemon XD gale of darkness. D-Throw has a hitbox that hits other characters like Mario and Luigi's Back Throw. I doubt that the D-throw -> U Smash string featured here is a guaranteed combo, but it looks like at lower percents (since they were apparently at high percents here) can set up some basic combos and strings
0:51 Confusion reflects projectiles properly!
0:53 We get a quick glance at Mewtwo's run speed here. It seems to be somewhere from average to fast
0:54 Shiny coloration is back
0:55 Psystrike!
1:01 Another new taunt
So overall, what's been found is Mewtwo has his Melee moveset and recovery preserved almost completely with very likely some minor tweaks to attack speed, damage, and knockback. I know hearing that is going to concern a lot of you about how good Mewtwo will be in Smash 4, but this isn't terrible by any means. Ness has all of his moves from Melee and he's top tier in Smash 4. I think what will make or break Mewtwo will be some simple stuff like weight, frame data, whether or not his Dthrow leads into combos, and whether or not Uthrow keeps its outstanding kill potential from Melee.
Hope this made for an interesting read for some of you.
looks to be a copy of his Melee self, except that he has gotten buffed. Hopefully, that is the case. 
