I can confirm, that you can basically switch sides every cooldown by placing the your circle directly in the gate. You can easily test this at the entrance of the violet hold. Open the gate and place your circle there. Let it close, teleport in and walk to either side.
But I'd like to warn you at Gothik - there are two holes at the angles of the gate where you cannot get out if you accidently walk in there. (Unless you teleport again after the cooldown)

Something additional:

In Warsong you can easily cap a heavily defended flag by placing your circle on the roof, jumping down, grabbing the flag and immediately teleport back. (This is even easier if you got slow fall. With this way you won't even touch the floor)

another trick is to use it as a feint
say you run up the tunnel, get to the speed buff area and place the portal
you run up snag the flag and run the the other way. people will follow you naturally, then suddenly *poof* gone and they cant see where you went

On Gluth a group I was with tried this

1 Lock stopped at end of poison tunnel and dropped his circle. Then jumped down and went to work gathering adds after he got quite a few he teleported back up to tunnel. and the adds followed him and stood at base of tunnel as he used rain of fire to keep their attention.

another lock placed his circle in the middle and gathered adds using his instant cast dots while running away from the tunnel. when he got to the other side he ported back to the middle using his circle and ran the group under the first locks rain of fire. ( soul shatter is a viable backup to help dump aggo but only once due to long CD)

Personally I use it in sarth to not only make my life avoiding walls easier but to mark the spot on the ground where its safe to stand

On Deconstructor use your demonic circle in the center and when you run away with the bomb, you can port back for increased dps.

UGGG WHY?!?!?

Depending on your strat, you could alternatively place it in the safe zone on the pull and more quickly minimize light bomb damage. Lost dps time due to running should be the same.

Yeah, that's what I do.

We use a 2-camp approach for the 10-man version. On the first debuff I get I run to the side (still in range of the boss) and drop my portal. It doesn't save time on the first debuff, but it does on later ones, and it's more important to get out of the group quickly than get back into the group quickly. It's also closer to add spawn sites on my side.

Some thoughts:

Council - Depends on the order, but place it on where you tank one or two of the mobs, as that's where power circles will form. Run out for overload and port back instantly.

Kologarn - Kite beams away and port back to your location.

Hodir - Place circle in a general centralized location to better cross the room to fires and other buffs.

Mimiron - Circle strafe the spin-up, then port back to your location.

Vezax - Same as hodir, really, pick a general centralized location to access green/black clouds

Auraiya - Port back to cluster after fear.

Yogg - Port either to or from Sanity beams.

Razorscale & Ignis - use it to port back on the ground after a wing buffet or flame jet.

no longer here

Kologarn - useful for running away when you're being targeted by eye beams, or you can put it in the middle of the raid to port back in after you've run out.

Freya - could use it on the phases where there's Nature's Fury and Sunbeam to get back into the general vicinity of the mushrooms.