I'm going to watch the whole thing, but based off the first 5 min, man you need to speed up your game. Yoshi can decimate people from all sides all the time. From what I've seen, you're thinking far too much and not fast enough. Also, I tell now players this alot (not assuming you're new in any regard) but you need to put purpose behind every move you throw out. Never just throw out a move just to have a hitbox out. That's something everyone needs to keep in mind, but you seem to have a problem with the second aspect of that, you don't know what to do to follow your moves. You need to know options and what to follow with depending on what option your opponent takes. In the vid, you landed dair on the pikachu multiple times and had no idea how to follow it up. Yes if it pops them up its an easy follow, but if they tech or SDI correctly or they're at low %'s you don't get that knockup. In those events you just sat in shield, which will get you killed very fast vs more savvy opponents. You have to have a though process of: "If I get this hit, here's how I make the most of it. If I don't get this hit, this is how I'll escape or this is how I'll make advantage of the shield pressure" or whatever.
3 things you need to take away for right now: Speed up your neutral game, you're not even close to being fast enough right now. Secondly, use grab more, Yoshi's grab is AMAZING and opportunities to use it are everywhere throughout Yoshi's Neutral game. Lastly you're approaches are very mediocre, you just fullhop aerial and hop to god that you get a hit. Grabs are a good way to get in, Shorthop backairs are decent for spacing and hit-confirming, eggroll is a good approach if you use it creatively enough. Tech chases will come with the combination of those and you'll find more interesting ways to hit-confirm off of your hits and wrack up damage on your opponents super fast.
ALSO, never do a full turnaround eggroll ever again. You used it twice. You CANNOT do that vs anyone with a brain, it is far too slow and it is ridiculously unsafe. Work eggroll into your game for recoveries and only to use it in short bursts on-stage, you almost never want to actually turn around in eggroll.
Here's some of my play as possible reference material:
http://www.twitch.tv/dannycake/b/533520584
http://www.twitch.tv/dannycake/b/533539349