This might be old by now (I originally noticed and mentioned it after the beta), but I haven't seen anyone mention it and now that I have the ability to record and share it, that's what I'm doing.
(Sorry about the title, it's not about an under-appreciated sci-fi show, small hamburgers, or a certain type of pitch in baseball; naming things is hard.)
The thing I found is a sort of movement mode. You hold the left stick (or the right stick if you use southpaw sticks) slightly forward and you hold the right stick to the left or right, and that makes your character sort of glide around. I call it the Hunter Slide because Hunters are the only class stylish enough to deserve it (and naming things is hard).

Here's a demonstration:
http://xboxdvr.com/gamer/Gnrl%20Vagueness/video/10397644

Here's a somewhat better one that also shows it with my character crouched:
http://xboxdvr.com/gamer/Gnrl%20Vagueness/video/10397642

I don't know if this happens in combat areas. If you move too fast or don't push the look stick over enough for it to register, the slide doesn't happen and you do a normal slow walk, which you can see happen in the videos above.

Because of the slow movement speed you can't go up certain stairs while sliding, and going down certain stairs or significant drops will interrupt your tranquil stance, as will trying to go up stairs that are too steep. Interestingly, not only does the walk animation not play, but idle animations play during this, so your character may look around, shift their weight, and so on while moving.

Since you need to be always looking to one side you'll slowly move in a circle. This makes it even less well-suited to long distance travel than slow walking, but you can make it work well enough. To do that you first push the right stick only slightly to one side, so you'll move in a relatively straight path. Once your character has drifted too far to the side you keep holding forward on the left stick and push the right stick farther to the side to swing the camera around to a different direction, which will make your character keep moving and keep facing the same direction, and then you hold the stick only slightly left or right of center again. This gives you a sort of meandering forward movement.

Nice. I do recall someone found it way back when (last year sometime), but I'm too lazy to search.

Was kind of hoping you were talking about this.

I "discovered" this months ago. I'm told that other people see you as twitching/jerking - they don't see the glide.

I have a controller on which the thumbstick doesn't return all the way to center, so I'm always "sliding" on accident. I watched my moves on our other screen, only to discover that to the rest of the world I look like I'm glitching instead of moonwalking like I smooth criminal.

Was kind of hoping you were talking about this.
[clip]

like I said, under-appreciated
I still have my entry to one of the DBO drawing things from last summer, I can't remember if anyone ever guessed it

I have a controller on which the thumbstick doesn't return all the way to center, so I'm always "sliding" on accident. I watched my moves on our other screen, only to discover that to the rest of the world I look like I'm glitching instead of moonwalking like I smooth criminal.

well crud
at least you can amuse yourself with it, I know I have