General mechanics:
¤ Slope boost
Dive into downward slope. Gain horizontal speed.
Alternate form: jump off downward slope. Gain horizontal speed. You can do this on curved surfaces too, like wheels.
Deliberate, but oh so abusable. Do it every time you get the opportunity.
¤ High jump
Move upwards along slope then jump. The jump momentum is added to your existing vertical momentum from moving along the slope, giving you more height from the jump than you normally would get.
This is how my version of the five-box skip works. It's also critical in all(?) of the skips that involve getting onto a ledge you'd normally need to go fetch a box to reach.
¤ Slope launch
Dive into downward slope, jump off into upward slope, fly off into the stratosphere. You can jump off the second slope to sacrifice horizontal momentum for vertical (see high jump), or avoid spikes.
You know those rotating boxes they love so much? Yeah. There's very few sections like that I don't skip half of.
¤ Corner boost
If you move along a surface (don't even have to be ¤on¤ it; it can even be a ceiling if you can get close enough to it) then puff just past it, you hit the edge and it gives you a speed boost in the direction you were traveling.
Finding a corner boost in a VERY unexpected location was the missing key to making my skip at the end of Cousin's Harbor consistent.
I think it's an unexpected effect of Leo's "squishy" hitbox interacting with the two surfaces of the corner, his mass rolling off one surface exerting extra force on the other.
¤ Wall climb
This is the only actual glitch I've been abusing. Some surfaces, when puffed against, push you upwards instead of outwards. Which surfaces do this appears completely arbitrary.
The most blatant is towards the end of Leo's Storm, which lets you scale most of the vertical length of the level and skip almost the entire moving platform section. This is also what's at play in the infamous dropping boxes skip in Olga's Contraptions.
I suspect a deliberate mechanic to help the player up onto some difficult ledges, but the "climbable" flag is misapplied in some cases.
Level-specific things I haven't seen others using:
¤ Visit the conductor
At the end of Victor's Trainsport. With a little run up (which can easily be done on the passenger cars) you can jump past the spikes on top of the engine and perch on its front. This lets you just ignore the autoscroller... but doesn't skip the actual scrolling. Still, free safety, and it gets you to the end of the level that much sooner. Jump off the train at the last minute to shave off a little more time.
¤ Sergej's Grindery death abuse
At the very beginning, the rotating broken windmill things are in a pretty bad point in their cycle when you get to them. But they reset to a more convenient point when you die. So... jump off the cliff.
¤ Blind saws
In the section of Station's Entrance where you have to move the lights around to see the saws you need to avoid... no, no you don't. Put your faith in The Cycle and it will deliver you to salvation. The saw on the far right and the background make a good visual cue for your position and the phase of the cycle.
And some things I found but either aren't consistent enough to use or don't have a use I can find:
¤ Leo Burger
Only managed to do this correctly once. If a box lands on top of Leo just past his center of mass, he gets launched horizontally. Easiest to get at the beginning of the five-box section; you can knock the first box up into the air and hopefully get into position underneath it before it lands. VERY precise. In that instance I suspect it's faster to just dive down the curve at the beginning of that big room anyway.
¤ Lunging saws skip
In the first instance of the lunging saws in Leo's Storm, you can jump over two at once with a little precision. To actually save time with this, you'd need to immediately pop out and get in front of the second saw, which is an extremely tight window, and THEN set up for the second very precise jump. I don't think I've ever actually executed the whole thing correctly.
¤ Jumping saws skip
Another twofer, this time in Engineer's Heart. The section with two columns of saws, one moving up and the other moving down, then they rapidly jump back and do it again. You can squeeze through the gap formed just before they jump back; it definitely should be doable to fly through then go back to the left to avoid the saw slamming down on you. I've been attempting it each run because the way the checkpoints are set up in that section make it basically free to try, but I consistently eat it after squeezing through the gap.
¤ Leapfrogging on the train obstacles
You can jump off the top of the posts in the Victor's Trainsport autoscroller. In theory, if you manage to carry enough momentum off the slope entering the area and very precisely bounce off them to keep off the tracks, you can basically skip the autoscroller. Good luck :)
¤ Boat pin
At the beginning of Victor's Den, if you get in front of the boat you're supposed to ride over and sit in front of where it stops, it'll pin you and you can't get out. Leo's sprite glitches out.
¤ Wife's Trail out of bounds
The only things that can kill you are things explicitly marked as "this kills you". This includes pits, which simply have a kill hitbox just offscreen. Except in one spot I've found. In the section where you have to use levers to jump over big saws, if after the third saw you miss the ledge and hug that wall, you don't die and just fall offscreen and out of the level. I haven't found a way back in bounds, or even to die. If you move far enough to the left/right, things get weird.
To add to the Corner Jump. I think all corners close or at 90 degrees can be jumped off of. There are skips involving corners and a surprisingly high amount of locations.
And now I have to attempt leapfrogging the trainsport obstacles. Thank you very much >:(
