I've TASed this game, so I know a few tricks to save some time, but I haven't proven all of them to be possible in a real run yet. But here they are for you to try if you're interested.

First, of course, here is my TAS of this game. All the tricks are in there. Note that I used v1.11 so the gameplay is slightly different and there is no Starry Sky Warp. https://youtu.be/cWbwspAL6cY

1. There is a frame perfect trick you can do right before the checkpoint of the first level. If you jump on the right frame on the slope and stomp the first goomba, it will give you a mega boost. Similar tricks can be done throughout the game, but since this one is in 1-1, it doesn't hurt to reset if you fail.

2. In both boss fights with Fuzzy, if you through the block while Fuzzy is invincible at the right time so that it clips inside him, you can hit him on the first frame he becomes vulnerable. Once when I was practicing this, I hit him, but the next time he started rolling he never stopped, which is interesting but I had to kill myself since there's no way to finish the fight.

3. You can slide with the penguin suit in Tangle Temple to move with very high speed, but the speed is very hard to maintain in real time and it's hard to control, so I'm ruling this one out, but you can still try it.

4. There are two spike ball skips in 1-Castle. The first one is the very first set of big spike balls you need to release to kill three piranha plants in your way, but if you have a penguin suit, freeze the small piranha plant on the top and it will fall down and kill the other two, then simply slide to kill the frozen one. Really easy. But the second one is very difficult. After you enter the pipe after the checkpoint, you need to spin at the right time and hold right to avoid the switch below the exit pipe. Then freeze the big piranha plant and kill it with a slide before it wiggles free. After that, you'll need to avoid the first two piranha plants and then get hit by the third one, then just run all the way through. The reason these skips save time is because spike balls move very slowly and it takes longer to wait.

5. In Fossil Tunnel, you can fly onto the top of the hill and skip the entire level. Everyone knows this one.

6. In Pyramid castle, after hitting the switch which makes two platforms rise from the sand, you can jump over the block that revives the first Thomp and get pass him through the narrow space between the Thomp and the wall. Saves a second.

7. This trick is not used in TAS. In Grimymole Mine, it's a good ideal to grab a Yoshi because you're very likely to get hit here (you don't get hit in TAS). When you flutter with Yoshi, don't hold any direction keys and Yoshi will flutter without slowing down. This is especially useful when clearing the huge pit after you get the star.

8. There is a major time save in the boss fights with the big mole. By ground pounding him while he is going back into the sand after his crazily throwing wrenches, it is possible to skip the animation of him dissapearing and reappearing and hit him instantly. This trick is very difficult to perform, and you're most likely to get hit when doing it.

9. In Bubble Basin, there is a section where you can jump out of the water. Do that, since Mario's speed is much faster when out of water than when underwater.

10. Similar to the boss mole glitch, there is a glitch you can do with the Ninja Shy Guy. After you stomp him once, he will go dizzy, and if you ground pound him at just the right time, you can hit him again. Surprisingly, this trick isn't all that hard. There is a big window of frames you can do this. I've already done it in my run.

11. In 4-A, you can clip through the wall after hitting the switch. Everyone knows this one.

12. In v1.00 of this game, you can skip Sky Mountain by going to the world select and go to Starry Skies. Everyone knows this one.

13. In the boss fight with Kamek, there is an easy way to manipulate his movement so you can finish him off quickly. After he does his magic and the blocks start moving, don't move at all. Kamek will start shooting fire the first time he appears and you can go stomp him. After the first hit, again, don't move at all. The next time Kamek appears he will shoot fire again, and you can stomp him again. I haven't found a way to manipulate the third hit yet, so he will dissapear for a few times, but you've already saved a truck load of time.

14. During the final battle, I suggest shooting Bowser from the back. It's safer, since Bowser only throws things in front of him, and you're less likely to get hit. Secondly, if you practice this enough, hitting him from the back is actully faster than hitting him from the front.

Anyway, I hope you find these helpful. I'd say a 1:42 is possible, and I'm going for it. Let me know what you think below.

Is the clip in 4-A possible with the propeller suit? iirc when I tried it, I could only get it to work as small mario, at which point I'm not sure it would be faster to damage down and enter World C without propeller.

+GreenUprooter You're right, it is only possible with small Mario, so my strat now is not to use the two propellers you purchase in the shop in Rubble Ruins before World C, do the clip as small Mario, then use the first propeller as soon as you enter World C. The other propeller is a backup for C-Tower if I get hit in the level before it. Then I will purchase more propellers for World 7 and 8 during the Starry Skies warp.
The clip saves fifteen seconds, and I probably only lost two seconds getting hit and then using the propeller on the map.

Similarly to the Yoshi's fast flutter, in 1-3, when you jump off a vine, stop holding any direction keys and you can keep your momentum. The momentum will carry on if you stomp a wiggler and continue to not press any direction keys, allowing two major speed boosts, the first one is stomping the wiggler below the first star coin after boosting off a vine, which is pretty easy. The second one is a lot more difficult, since you have to boost off a vine and stomp three wigglers consecutively to get a long boost.