As far as I know, the Attraction Train is just for fun, but I wouldn't know exactly since I don't have anyone to play it with T_T
And a few tips for Octopus Dance: when the little octopus appears, you can touch the touch screen to make him smaller; if you do this three times when he's about to spit ink, he will barely spit any ink, so you can still look at the Gamepad screen (and I'm pretty sure it still counts for the 3 Inky Moves stamp).
For the 50 Perfects stamp, they don't have to be in a row, so if you miss a few, any perfects you get in the extra stage will count towards it.
Sometimes there will be hearts floating around, and you can grab them by either touching them on the Gamepad or with a Wii Remote.
And last (and this is kinda obvious) in the extra stage, the number on the diver's head is how many beats there will be next, and it will only be 1,2,3,5, and 7. For 1,2 3, and 5, you will do three dance moves, and 7 will have four. There are no extra hearts on the extra stage.