Some preliminary things...
- Koji Kondo composed all the original songs. Hiroshi Okubo is the arrangement supervisor.
- Your notes are flipped oddly in a lot of places. Rule of thumb is the stems should face away from the note furthest from the center of the staff. So that means m. 3-4 (RH) should be flipped. Look out for other places as well.
- Rhythm groupings - when dealing with rhythms involving 16th notes always be sure to show every beat. So m. 55+ will need to be fixed, as beat 4 is obscured.
Now to start looking at the beginning...
- Harmonies wrong in m. 1-2. Specifically beats 3-4 are parallel sixths, not fifths. What you have for beats 1-2 would work since it's in the right chord but, definitely need to change the bottom notes in 3-4.
- m. 3-4 - LH an octave too high. If that was by choice, you still need to be consistent with the rest of the sheet. It jumps back down to its original octave in m. 5.
- In this section I would strongly suggest cutting out the middle note in each of the RH chords for two reasons - this makes the sheet sound "lighter" like the original, and successive chords are more difficult and tiring to play than just dyads.
- Some notes definitely need staccatos. Like the first note of m. 6. See other places in the picture.
- Biggest issue - harmonies in general. I've re-transcribed m. 9-12 quickly and got something more along the lines of what you see above.
Given everything that I've found at the beginning I would strongly suggest giving the whole sheet another close look.