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I would think that the best example is: if you just walk off the end in "Free Your Mind" and keep going, you'll make it over the first obstacle every time. It took me many failed attempts to work out this easy way.

I find there are a number of aspects of the game's behaviour which just don't seem predictable and it makes life incredibly frustrating in time-trials. There are a number of places where there's a really fast line but it seems like the game only allows it half the time -- so either I take the risk and lose most of my attempts to (seemingly) arbitrary failure, or I don't take the risk and get a worse time.

Here are some specific examples:

* 9 o'clock news: sometimes you can walk straight off and through the first gap in Vertigo, sometimes you just don't make it and die instead. It might be something to do with the speed you've reached before you walk off the ledge, since if you get a bigger runup you're more likely to make it, but it's not a simple relationship.
* From In the margins to final challenge: sometimes you can walk straight out and miss the spikes on the first ledge. This *doesn't* seem to be a speed thing; in fact, the further you are from the edge when you start walking, the more likely you are to hit the spikes.
* Three's company: sometimes you go further through the first rubber band than you expect, causing you to overshoot your jump.
* Then there's Souleye's description of a similar problem in I'm Sorry.

Does anyone have any idea why these strange behaviours exist? Is the game nondeterministic, or is there some other explanation? 

To add onto that, maybe co-op levels. And to further add to Terry's coding hell, collision detection between the players

How would player collision make sense for mid-air collisions? If Veridian falls downward and Violet falls upward and they meet in the middle, do they counterbalance each other and just float in space? Veridian walking on Violet's feet and vice versa? It bends my mind just thinking about it...

Here are some more 8-bit references:
Manic Mine: Manic Miner for the ZX Spectrum [although I think the Yes Men is the most similar room to MM in the game]
It's a Secret to Nobody: Secrets in Legend of Zelda on the NES were marked with "It's a secret to everybody".
Sweeney's Maze: ZZT by Tim Sweeney of Epic Megagames (now famous for Unreal). The monsters here are centipedes from ZZT.
Twisty Little Passages: Zork/Adventure type games

And non-gaming references:
Silverstone Grand V: Silverstone is the usual track for the British F1 Grand Prix
Take the Red Pill: The Matrix
Ascending and Descending: MC Escher picture of the same name
It's not easy being green: Kermit the Frog! 
Green Dudes can't Flip: White men can't jump
Murdering Twinmaker: The Fly

and that's only from two levels  anyone want to do some of the rest of the game?

Also, I like the music track that you get in the Tower in Flip Mode  Spoiler: It's in the jukebox as ercoF evitisoP