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.
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.
Start climbing up or down a ladder, stop, then climb again. Mario will climb the ladder faster.
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.