It is impossible to do a play-through containing all 6 different types of stages. The most you can do is five.
You cannot do both schools of fish in one playthrough. Conversely, you can only do the second tadpole after you have done the first.
Octopi and anemones can be caught. Buckets and nets can be caught as well.
You get a boost in score if you defeat the schools of fish quickly, if you catch all the tadpoles before each pass is over (or run into them), and if you catch all crabs before each pass is over.
Field 28 cannot be accessed until you complete Field 8. Also, if you are headed towards a different end field and almost at the end, you go to that end field after the 30 minute mark.
There are two instances of going back a field in terms of numbering. One is Field 40 to 35. The other is Field 42 to 26.
Certain field numbers are skipped.
You actually have an invisible .99 seconds on the timer that isn't seen in the Super Famicom version. You only see it in the remakes.
In Field 47, you have a chance two encounter two flopping fish... or none.
Can you name more interesting and obscure facts?
There's a bunch of unused enemies in all versions of the game - including the DS port and the Steam version!
The DS, Vita and PC versions will reliably crash on field 45, if you're hooked onto the leftmost part of the bridge as it starts to break.
Oh, wait... you said fun facts. Never mind.