Well guys, thanks to your advice, I was able to complete the 1st World 125 frames faster (not compared to the original, but to the 1st improved run), I'm also happy to say that every level was improved (except for the castle, which I ended up even). The improvements mainly come from corner boosting wherever possible and just using the 1st hill in 1-2.
http://dehacked.2y.net/microstorage.php/info/1191593279/Super%20Mario%20Bros%203b4.fcm
Individual level comments:
1-1: Saved 6 frames due to corner boosting. 1 cb opportunity wasn't taken cause I like going up in the clouds. :)
1-2: Biggest improvement by far. To be more entertaining, I go through the level backwards. (the hammer bro was being an ass though, which is why I delay grabbing the thing at the end.)
Fortress: Same as before, with 2 cb's.
Hammer bros: 5 frames faster.
1-5: Basically same as before. I get a bit lucky with freebie frames here.
1-6: 1 cb was barely possible, other than that, not much different.
Castle: I'm pretty sure this can't be any faster.
I really appreciate everyone helping me out. Especially JXQ, for all his knowledge from doing the warpless run, P.J, for pointing out a trick I didn't know, and Tompa, who showed me that even when it looks perfect, it might still have room for improvement.
Based on the respones, I've decided to continue with my original plan and only use B for items.
May I continue to World 2 now? :)