The combos weren't terribly impressive as said earlier - and some of the combos and even movment seemed a tad jerky and umpolished (Y. Link falling off-stage after his d-air, Bowser about to get edge-hogged by mario when he was trying to fortress-hog across Yoshi's Story, stuff like that). Personally, I thought the segments featuring Mario and Doc were the best (incidentally, these were also the longest I believe, some of the clips were a tad short).
I do like the video though, and it's because of the comedy aspects of the video you've mentioned above. To me, at least, it seemed like you had a lot of fun making this, and didn't take it too seriously. Hopefully, as a crew you'll be to improve, and you'll be to make entertaining as well as technically impressive vids.
I'll give it a second watch with more specific criticism, I know I was rather vague.
*Edit* As mentioned earlier, chain-throwing is usually seen as rather bland for combo videos, unless the throws eventually lead to a combo (Marth CG on spacies to u-tilts -> F-smash is an example).
- The Doc combo that begins at 0:26 is what I meant earlier by "a tad jerky and unpolished". dash attack to missed d-smash to d-smash to cape to a u-smash-> u-air. The missed d-smash and ending a combo with a combo-ing tool (u-air) just seems a little abrupt, and kind of leaves the viewer hanging.
- The Y. Link Combo at 1:14 was good, even if it didn't result in a KO. Showed a player's reaction to a shielding opponent that resulted in a combo that seemed thought out.
- IC semi-juggle at 1:55, an okay string of attacks, but I still feel left hanging especially when a weaker hit like u-air is the finisher.
I think that covers the major points without being repetive/nitpicky. Hope I didn't sound mean, those were just what stood out to me the most that could be improved.