Medical Pavilion *

Vita-chambers

1. As soon as you enter, on your left.
2. In the room with the shotgun on the floor.
3. In the room where the sign is blown up.

Normal Progression

Grab the first aid kit and machine gun ammo on the desk before running past the splicers, letting them fight each other, and hit the first switch.

Can be skipped by hitting the wheelchair at the very beginning over underneath 
the window, standing on top, hitting out the glass, and flipping the switch 
from the other side, like cortez does.  Also skips the ambush you get when you
flip the switch normally, which is kinda nice. Tough to pull off quickly.

Shoot the window out on your way to the second switch. Pull it, and jump out the window.

Trigger ghost.

A good time to back up and collect whatever you can. You're stuck waiting.

After ghost is finished, push button to open door.

Go along the left side of the area ahead through the archway with a torch above it, grabbing the EVE Hypo on the ground as you go. Let the splicer at the door blow up, then run past the Nitro Splicer, up the stairs. Crawl into the hole to get Incinerate, turn around and run back out to the arch with the torch.

Melt ice downstairs.

Incinerate can be skipped by bashing a flaming object onto the ice with 
the wrench. This is hard since the only usable source of fire that is 
known is the burning corpse of the splicer who gets blown up by her 
ex-boyfriend outside Eternal Flame.
Current thinking is that the best method for this trick is to leave the 
thuggish splicer you pass on your right as you head to the Eternal Flame 
entrance alive to chase you - once she's close enough, the splicer who 
explodes will become alerted and turn to face you. Then look at her, 
activating the look trigger that explodes her. With luck, her corpse will 
land on or close to the stairs. Now light the bucket and bash it down to 
the Dandy Dentals ice.

Collect Telekinesis.

Just after you melt the ice, a splicer throws a table at you. This is the Magic Table Of Flight. It is important,
mainly because its physics become subtly different to other objects in the game after it gets thrown.

Normal progress from here is as follows:

Use Telekinesis to catch a Nitro Splicer's explosive, then use it on the sign.

Run up to Steinman's window, wait until he starts talking, then loot the room.

Kill Steinman and collect his key. (Telekinesis on propane tanks is advised. Headshots do increase telekenisis damage like anything else)

Optional: Go through break in tunnel to cutscene with Little Sister, rescue or
harvest the Little Sister. Select the Gatherer's Garden to open the exit.
Pros: You gain 80 or 160 ADAM, as well as random loot. Usually includes bandages, 2 
First Aid Kits and an EVE hypo plus some pistol bullets. 
Cons: You lose about one minute and fifty seconds.
If you chose to skip the cutscene, either die against the far door to spawn down in 
Dandy Dentals, or deactivate a bot in the doorway to prop the door open.

Return to the first switch and activate it.

Exit via bathysphere.

However, with the Magic Table Of Flight, things are different.

As you leave Dandy Dentals, take the Magic Table Of Flight with you. Because 
it remains solid while being held by telekinesis, you can repeatedly jump on 
it in midair to climb to unlimited heights. Use it to jump up the stairs instead 
of walking up them, and head to Aesthetic Ideals. When you go through the last 
door before your first meeting with Steinman, there is a wall in front of you, 
but it does not reach the ceiling. Use the Table to get over this wall. This 
avoids the trigger that activates the Vita Chamber in this room. Drop down on 
the other side of the invisible wall in front of the doorway Steinman blocks 
with debris, skipping clearing it. Also use the table to jump over the gate 
immediately afterwards. You can now ditch the table.
Progress to Steinman, kill him and take his key as normal. Suicide, and respawn 
at the Vita Chamber in Dandy Dentals. Do not leave Dandy Dentals; instead, 
run in the direction of the level start, into the flooded room near 
Telekinesis. Suicide again, respawning at the Vita Chamber at the level start. 
Now leave as normal.

Useful Death Warps

If you are skipping the sequence with the Little Sister, go all the way down the broken tunnel and drag some splicers with you. You need to be pressed into the corner of the door on the right side, if you are facing the door. Another possibility is to throw remaining propane tanks at yourself, or electrocute yourself in the water.

If you are not skipping the sequence with the Little Sister, warp as soon as you get Steinman's key. There are propane tanks in that room and one down in the pool of water, not to mention the pool of water itself. You will come out in the room where you blew up the sign and the swarm of splicers won't spawn.

Skipping Incinerate!

Melting the ice at the entrance to Dandy Dentals is necessary, so must be done using normal fire to skip Incinerate! The only sources of normal fire in the level are the Eternal Flame sign, the fire at the entrance to Eternal Flame, the burning body of a splicer who is killed in a scripted sequence when you approach Eternal Flame, and any body killed by an exploding fire extinguisher. The fastest method of melting the ice that is known to be possible is to set a small object (such as a nearby ashtray or the nearby bucket) alight using the burning splicer at Eternal Flame, then to quickly move that object to the ice that needs to be melted by attacking it with weapons or electrobolt.

ExplodingCabbage's notes on it: [1] [2]

Skipping Telekinesis

So far a way has not been found to skip Telekinesis.

The splicer who blows up the sign can not be killed.

The opening under the sign before it is blown up is an invisible barrier.

Explosives that have not been handled with Telekinesis will not blow up the sign.

Skipping Telekinesis is of VERY questionable value, considering how useful it is later on.

Audio Skips

None, surprisingly enough. Every audio message that plays either isn't holding anything up, or is ambient and unskippable. The only two messages worth skipping (at the end of the little Harvest/Rescue drama) are avoided by the death warp.

Notes

"Ran to the bot stuck in the door and hacked it. You can't blow it up - I tried. " - Cauldrath

Cauldrath's notes on his first run: [3]

ExplodingCabbage's notes on propping open a door or two: [4]