I was able to improve some levels and also found a really weird glitch that doesn't seem to serve any purpose (you'll see what I mean if you watch it). I don't remember seeing any of these things in this topic already, so here goes.
Here is the really weird glitch. I did it in 2-2, don't know if it would work other places too. It includes misbehaving sprites and objects, and a misbehaving game. After I beat the level it auto-joins the next level and then auto-resets. Also my extra life count jumps from 21 to ~53 or something like that in the bonus game. If you die due to timeout the time-out message is broken (not shown) and then it will auto-join the level and auto-reset. After the level is completed, if you press any buttons before it auto-resets, it will reset. Again, this serves no purpose that I could see besides being nifty.
Here is level 0-3 improved by something like 44 frames (based on when the next level is entered so it accounts for less good placement on the finish stand).
Here is 5-10 (tall pyramid level) strategy unoptimized. It would probably be better to place the girder one spot higher so there is only one key grab needed in the end. This demo is mostly just to show a backflip off the wall, which might save some frames in many levels.
Edit: I just saw that Omni did the backflip off the wall in his old wip on the first Kong fight in the Plane.
Here is an improved strategy for 2-6. I think it's something like ~5 seconds faster, but not entirely sure.
Also good to know, when going to a door exit, jumping at the door can be one frame faster if you jump at the correct frame. This is not shown in any of my demos.
EDIT: It turns out this applies to jumping in general (anywhere) rather than just when approaching exit doors, although with exit doors it seems to me like it can be more than one frame faster.