Here's the trailer, which I will be posting two of (one is my upload, one is another person's). In the event that one of them is flagged, simply watch the other. Both are in HD. Below will be my analysis of the trailer, which may be subject to further revision and/or improvement after initial posting. Also, Serah being epic, as well as Serah's new outfit (and Noel, who is also epic) for the win.
Mine
Theirs
The full HD video of the official trailer shown at E3 within the last hour or so. It depicts all of the scenes found in the short teaser trailer from before, as well as new cutscenes. In doing so, it reveals what Noel's English voice actor will sound like, as well as a plot detail; from what Lightning says, it may be inferred that everyone assumes she is dead, when in fact they have just forgotten her, all except for Serah, that is. Noel's surname is also revealed, and a remix of the track "Blinded by Light" plays during the trailer, implying the music in the new game will feature remixed tracks from FFXIII (though it won't likely contain only remixes). Finally, a new combat feature was displayed, at 1:30, called "Cinematic Action". This was directly followed up by Lightning riding on Odin in Gestalt Mode, confirming she still has access to her Eidolon, as well as showcasing a new means of using Gestalt Mode, where in you use turn-based gameplay during a cutscene of sorts, no doubt inspired by the aformentioned "Action Cinematic" system. What is interesting to note is that the battle HUD indicates that she is fighting against "Chaos Bahamut", which may be present in the trailer to prompt thought from the viewers, specifically as to why an Eidolon belonging to Fang, Lightning's friend, would fight her, or why she would fight it. Whether an Eidolon becomes an independent entity of sorts, and thus develops unpredictable behavior, can only be speculated upon at this point. The fact that a girl mentioned to Serah that her friend died trying to escape from the Purge, a key plot device in the Final Fantasy XIII that sets the story in motion, also suggests that not only will new story elements be introduced, by older elements, and their respective themes, will be touched upon as well. The main characters, aside from Lightning and Serah, as well as the newly-introduced Noel, also do not appear. Lightning's apparent playability implies that the others will be playable as well, though the reason for not showing the others in the trailer may be to focus on the new primary deuteragonists, Serah and Noel. Team Nora appearing to be directing everyone begs the question as to where Snow is, especially since, based on characterization from the first game, he would never let her go on a "quest" of sorts, such as the one in this game, without him. This may be attributed to the "memory loss' mentioned by Lightning, though cannot be confirmed at this point.
During a few scenes (particularly @ 1:20 and 1:24), a Pulseworker, a usual enemy, is listed amongst the names of the characters under the player's control, as well as a Feral Behemoth in the next scene. How players will bring them under their control, as well as whether it will only apply to specific creatures, and/or only be available under set conditions, remains unknown. @ 1:25, the "Cinematic Action" is shown again. Given that the enemy doesn't seem to be a substantial boss of sorts, it may be safe to assume that the Cinematic Action can be triggered during any battle. Whether the mechanics for triggering it remain the same between regular or boss battles isn't clear, though, Noel was shown asking Serah if she was alright shortly before the first Cinematic Action, suggesting it will, at the very least, help with characterization and plot development, if not being dependent on it. The enemy both Serah and Noel battle during said scene (@ 0:51) bears some resemblance to a creature from Final Fantasy XIII, though, for those of you who are aware of what I'm referring to, please abstain from posting it in the comments, out of courtesy for those who have yet to complete the game. From an aesthetic point of view, the HUD seems to have been re-designed, at least during battles, having blue as a more prominent colour, distinguishing itself from the gray colouration of that found in Final Fantasy XIII. Noel's likeness to Fang, based on the clothes he wears, may be evident that he comes from the same Gran Pulse that Fang does, though the naming conventions he uses for himself contradict this (it is possible that he is merely omitting it from what he mentions, though). @ 0:36, Noel's lip movements in particular also suggest that, like in Final Fantasy XIII, the animations will be completely re-done for the North American version (which was totally awesome).