Time to clear up a couple of things here =).

First off: The definition of cheating is breaking the rules set for what you are doing. When you compare a Real Time Speedrun to a Tool Assisted Speedrun you need to start off by knowing that they are two very seperated things. They have different goals, show different skills and have two completely different ways of making. If you follow the rules, you are by fact not cheating.
While a TAS is done on an emulator with slow motion gameplay and save states, the game is never altered in any way. It behaves and plays the same way as on console (With minor differences to the amount of lag and loading times).
Time to point out a couple of things in this TAS:

1. The hitboxes. These are really bad when it comes to the piranha plants for example. Here you can see how bad they really are: https://www.youtube.com/watch?v=hoUmUs9PeI0&feature=player_detailpage#t=85 Jumping through the flowers aren't cheating, it's not a glitch, it doesn't require you to make a TAS, it is simply nothing strange at all. Just how they decided to make the game.

2. Walking through walls at 0:25 is a glitch. Glitches are allowed in speedrunning and TASing because they are a part of the game, considering they can be done in the game without any modifications to it. That glitch, and similar wall-glitches, can all be done non-TAS as well.

3. At 0:30 you already read my answer to it, so I won't mention the same thing again =). The other enemies you mention is again just a part of the game's hitbox detection. Bowser's Hammers are a special case even. Because he throws that many hammers at once, the game can't process them all quickly enough. This results into some of them not having a working hitbox at first: http://i.imgur.com/hBB91Us.png So if you jump through the inactive hammers, you won't get hurt. Though shortly afterwards, they will all be working and kan kill you: http://i.imgur.com/T4mKIAF.png
Also notice that despite the hammers spinning, the hitbox always stays at the same place.

4. 0:37 Normally, as you probably know, you have to take the beanstalk in order to reach the warpzone. The way this works is that the game can't have the "loading zone" of both where the beanstalk takes you and the pipe take you, at the same time. The TAS changed the camera position, which is the reason for jumping through the walls, to have both these zones active at the same time. So when you then go down the pipe, the game is tricked into believing you took the beanstalk. This is, again, just a glitch that anyone can do with some practice and understanding of how it works.

5. 0:41 This is a Wall Jump Glitch. It's done by having Mario land on the 16th pixel of a wall and then performing a one frame jump. This is a common glitch in the 2D Mario titles. And works practically the same way in Super Mario Bros. 3, Super Mario World, Yoshi's Island, New Super Mario Bros. and more. Real time runners use this as well, it's perfectly legit.

6: 0:51. When you approach this flower, it will always disappear in the NES version. You can't get killed by it. This is not a glitch but just how the game was programmed.

A general thing about the video, it should obviously have been mentioned more clear that it is a Tool Assisted Speedrun. We don't display these are World Records normally. Why the uploader, which is NOT the maker of the TAS, did this, I have no idea. But the actual World Record, which is even featured in Guinness World Records, is the following: https://www.youtube.com/watch?v=JQ24UHbhFM8