Have Mario jump when a barrel is passing directly overhead at the end of a ramp. Points will be awarded as if Mario actually jumped over that barrel. Note: This works particularly well when Mario is on the ramp directly below Donkey Kong.
Faster ladder climbing
Start climbing up or down a ladder, stop, then climb again. Mario will climb the ladder faster.
Invisible wall
There is an invisible wall near the second hammer on the left side of the "rivets" level. Mario can bounce off the wall to grab the hammer without falling.
Lost hammer
On the "ramps" level, take a hammer and destroy a few barrels. Move to the edge of a ramp and fall to ramp directly below. Mario will not lose a life, but his hammer will disappear.
Teleport
Move Mario up the first broken ladder on the "ramps" level, then climb back down. Walk to the left and position Mario so that his back is almost touching the same broken ladder. Then, move him one or two steps to the right and jump. If done correctly, Mario will fall through the bottom and appear in the "rivets" level or re-appear after several seconds on the top ramp next to Donkey Kong. Note: This only works on some versions of the cartridge.
In the "elevators" level, move to the top right part of the screen to where the purse is located. Position Mario directly above the short ladder and quickly move him up and down to pass through the metal floor.