I'm going to go back in time to segments 3 and 5.
Segment 3: Before the first rock formation, there's a secret path behind the background, that takes you up to the rolling guys on the hill. Might save some time by skipping the spin blocks, but I haven't timed it.
Segment 5: When you have to get the key in the U of blocks, you can save yourself two flips. The key is hidden in an alcove in the back wall. Jump in, jump out, save a few flips.
Edit - I've watched through segment 13 now, and you can save some major time in 3-1. Before the red pipes, hit the block that creates the ladder to where you fight Mega Koopa. Instead of going through the door, use Peach, and float to the platform above the red pipes. That pipe takes you straight to the end of the underground area, allowing you to skip it almost entirely.
Segment 14 - Flip earlier when you go for the posts, so you don't have to backtrack for the one. Plus, remember that water stops your pound when fighting Blooper. You could probably save a few seconds here.
Segment 3: Before the first rock formation, there's a secret path behind the background, that takes you up to the rolling guys on the hill. Might save some time by skipping the spin blocks, but I haven't timed it.
Segment 5: When you have to get the key in the U of blocks, you can save yourself two flips. The key is hidden in an alcove in the back wall. Jump in, jump out, save a few flips.
Edit - I've watched through segment 13 now, and you can save some major time in 3-1. Before the red pipes, hit the block that creates the ladder to where you fight Mega Koopa. Instead of going through the door, use Peach, and float to the platform above the red pipes. That pipe takes you straight to the end of the underground area, allowing you to skip it almost entirely.
Segment 14 - Flip earlier when you go for the posts, so you don't have to backtrack for the one. Plus, remember that water stops your pound when fighting Blooper. You could probably save a few seconds here.