*After a damage boost you will be invincible for 80 frames. It can be used for things such as walking over spikes or through additional enemies and will help to reduce lag on some screens since your sprite does not need to be drawn every frame. The counter is at CPU-bus: 0x0000bc

*Stairs slow you down, therefore, as little time as possible should be spent on them.

*Stairs are tile collision events that can interact with sprites. I think the game is programmed that Simon's x y coordinate can look onto the diagonal of the stair tile.