Super Mario World is a game with an enormous amount of known tricks. Even though this page is far from perfect, you should read up the SMW game resources: http://tasvideos.org/GameResources/SNES/SuperMarioWorld.html
Also, I suggest watching the currently published warps TAS to compare with your first attempt: http://tasvideos.org/3019M.html
If you are having so much problems with Bizhawk, as I heard you speaking in the video, just try using lsnes for now. If for some reason you are not able to edit some parts with your run with TAStudio, it's not really viable to use it. This kind of errors shouldn't happen, though. Did you install all the pre-requisites?
About the run itself, there are of course a lot of things that could be improved. I'm pretty sure every level is actually done faster by real time speedrunners, so, for now, it's a good idea to watch some speedruns to see how you could have gone faster. In a TAS, there are a lot of level specific tricks one can use to go faster that aren't viable in a real time speedrun. For example, you can item swap the goal tape in YI2, duplicate blocks to get wings in YI3, perform stun glitch to spawn a boss in YI4, etc. These are very complex glitches, so I suggest you to first try to understand the simpler stuff, such as speed manipulation and routing your levels better. Get the smw-tas lua script to start learning how the game mechanics work.
Also, I'm sure you 'rushed' a lot the making of this TAS. Keep in mind this is not the way to make an optimal run, you need to be very patient. As SMW is a complex game, it usually takes months to make a very optimal run. Of course you won't spend that much time in your first runs as you still didn't get into how the game works, but don't try to just do it in a couple days. Again, be patient and think of ways to save every frame you can.
Thank you, I realized that I was using a very old version of BizHawk and I just wanted to test out how Tas'ing works
Hey I made a test TAS video. I'm really new at this cind of stuff but if you guys are willing to give me some feedback I would really appreciate it!
Video Link