TWO Bonus Areas in World 1-3!
#1 In the part with the green pipe with a Piranha Plant, and a yellow pipe next to it. Walk right and you'll find out the yellow pipe is actually made of two pipes. Go through the one you're standing on.
#2 As mini (NOT SMALL) Mario you can walk through some of the horizontal pipes. In one there's a secret warp if you walk!
More tricks, tips and cheats for this game are right here - New Super Mario Bros cheats