Warp To The Cape
Start the game as usual, but don't go down the tunnel at the beginning of the first stage. Instead, hop over the gap and stop at the first flower. Jump on the flower four times as quickly as you can and you'll warp to the Cape.

Warp To China Place
In the first level on Cape Canaveral, go to the triangular elevators and get up onto the box on ropes, cross the falling platforms, and onto the magnetic jewel thing (it's that purple box with the magnet on it.) Jump 4 times on it and there you are in China... (There are no further warps in the game, I have searched it thoroughly many times.)

Warp To Africa
Jump 4 times quickly over the monster maker in the second level.