Sure, hey, I'll give this a look.
First of all, is there any particular reason you wrote out the whole repeat instead of utilizing repeat signs?
Second, while your rhythms are accurate durationally
(for the most part), they're not quite written the best way notationally
, if that makes sense. In writing music you generally want to make the beat as clear to the performer as possible, which in a piece of 4/4 music means making every beat visible in some way, through the use of ties (excepting certain easy-to-understand rhythms like a syncopated eighth-quarter-eighth, a dotted quarter-eighth, or a half note). So, for instance, in measure 5, you're probably better off writing what you currently have as a beamed sixteenth-eighth-dotted eighth, as sixteenth-eighth-eighth (that is then tied to a sixteenth).
Related, during the segment that starts at 1:34 in your Youtube link (idk what the theme is called, it's the one that's remixed as the wing cap theme in SM64), the rhythm of the bass seems to be slightly off.
I haven't done a thorough comparison of your pitches to the original - I usually leave that up to other arrangers - but assuming that the pitches are, indeed, correct, there's a couple of places where you have the wrong enharmonic spelling. In m. 5 and 7 (and anyplace that looks like either of those measures) the Gb should be an F#. Same in m. 13, Gb should be F#. Also I'm pretty sure the G in the LH in m. 66 should be an F#, and the B at the end of m. 20 should be a Bb.
Finally, if you intend to submit this to the site, there are some formatting considerations to keep in mind, which can be found here.
-Missing measure numbers
-First system not indented
-"Piano" marking visible all the time
-Some of the text is misaligned; arranger name falls off page, copyright info is misaligned, metronome marking overlaps music, composer name in the wrong place; music overlaps the latter pages' titles
Since it's your first arrangement and I've mentioned a lot of things here, I decided to go ahead and clean it up for you (and also incorporate repeats, but you're free to change that if you're not a fan). Here is the updated file: https://www.dropbox.com/s/wq7l4653p39bels/medley%20edit.mus?dl=0
There's also just general arrangement considerations. It looks like you didn't use articulations anywhere throughout the sheet; while they're not strictly necessary, I can definitely hear a few places where they would help to make the arrangement pop a little bit (such as the very first measure!) This is also a bit of a sparse arrangement; for instance, I definitely hear more music at measure 9 compared to 5, but they're written the same way. Additionally, the section starting at m. 27 sounds a bit thick and almost legato because of the lack of articulation.
Also, have you thought about incorporating some of the other parts into the score? I can hear, for instance, some parts in the trombone at mm. 14-15 that don't seem to be represented. Also, the empty half-measure at the beginning and the empty measure midway through are, well, empty. I know they're percussion, but sometimes it's possible to put percussion into the piano scores, either by requiring the player to tap something, or by replacing non-pitched percussion with pitches that fit the key. I'm not too good at percussion additions, so I can't really suggest anything; I'm sure some other arrangers might have better ideas than me on what to do.
I know it sounds like I'm picking on it a lot, but I'm really not - overall this is a pretty impressive arrangement for a first go in arranging, so congratulations! Keep arranging more in the future.