These are the boss notes. Due to the size of the description - I couldn't include this within the description itself.
This article is done in the order of the video.
These aren't necessarily bad boss fights, but the video merely showcases exploits that can be performed on them.
Dumb bosses are thrown in the mix too.

Sonic 3

Angel Island Act 2 Boss

Type: "You're too slow!"
Description:
With a nicely timed jump, it is possible to kill this boss before it can even move.
The timing is pretty exact, so this may take a few tries. Only try this using Tails or Knuckles, or if Sonic has the Fire or Lightning shield. (Although if you have a fire shield, this boss can't even HURT you...)
Difficult to Pull Off?: Sorta. Takes practice.

Midnight Resistance

Stage 1 Boss

Type: AI Glitch
Description:
Apparently the tank's gunner finds the sky more interesting than the guy shooting him.
This odd glitch is triggered by sitting on the ladder and jumping off at the last second - for what-ever reason, the gunner no longer aims at you. Viola. One non-threatening boss!
Difficult to Pull Off?: Not really. I triggered this the very first time I played the game.

Gleylancer

Stage 5 Boss

Type: Dumb Safespot!
Description:
This boss cannot fire behind itself, nor does it's movement pattern come close to the edge of the screen, allowing the player to sit behind it. This actually shows how lenient the player's hitbox is, more than anything else. With a good Option setup, this boss really cannot kill you.
Difficult to Pull Off?: This thing literarily cannot hit you whilst you are behind it. What do you think?

Golden Axe

Dungeon Boss - General Bitter x2

Type: Design Boo boo.
Description:
You'd think being Death Bringer's top guards, they'd pick a better spot to battle.
Nope.
This entire level is pretty much a "Design Boo boo", and is ironically the easiest in the game. The fact the boss can be triggered whilst by the pit shows this stage was rushed. I doubt it was intentional.
Difficult to Pull Off?: No way. Just get on to their right, and they'll fall in easily enough. Do not scroll the screen too far though.

Sparkster

Stage 1 - Mid Boss 2

Type: Unusual Strategy + Exploiting Developer Kindness
Description:
Only the hands of this guy (and projectiles) can hurt you. You can take advantage of this by timing your spin jumps and hitting the boss before it can do anything.
Difficult to Pull Off?: It's easy once you get the timing down. Just pay attention to the sound effects.

Valis

Ice World Boss

Type: Dumb AI + Exploiting Developer Kindness
Description:
Staying on the left of the screen will cause this bird lady to do... well.. the same thing over and over again.
When she comes over to your side of the screen, use a magical attack and she'll bypass you. This will also destroy any wandering projectiles.
Difficult to Pull Off?: Nope. Your timing of the magical attack doesn't even have to be that good.

Grandia X

Stage 4 Boss

Type: Wtf?
Description:
I don't know how to describe this. Was this intentional? The fact the boss constantly screws up whilst you hug the wall seems to suggest no..
When you fire into the wall of this boss arena, your shots will bounce backwards. By shooting ahead and "hugging" the wall, you can go behind the boss and fire directly into the ship, rather than having to rebound the shots from the bottom.
As for the black area - that's a pit. You're supposed to fall in. But if you hug the wall.. you.. don't.
If this was intentional, this has to be one of the most cryptic shoot'em up bosses in history. You are not introduced to anything like this in the game, before or after this fight. I found out about this by accident.
I really don't know
Difficult to Pull Off?: No... but.. seriously, wtf?

Sonic and Knuckles

Sky Sanctuary Mid-Boss 2

Type: Design Boo Boo
Description:
Developer 1: "Hey I've just ported over the Metropolis boss from Sonic 2, for the Sky Sanctuary level."
Developer 2: "Ooo, nasty. Hey did you adjust the boss' height so the player can't hit him whilst he's in the air? You know Sonic's second spin really adds to his reach."
Developer 1: "Sonic has a second spin?"
Difficult to Pull Off?: Get one hit on him, and he's toast. Tails can also use his, erm, tails, to helicopter into the boss.
Poor Knuckles has to fight this thing normally.

Double Dragon

Stage 1 Boss

Type: Dumb AI
Description:
Does this guy really count as a boss? You fight him as a normal enemy earlier in the level...
Regardless, once you've grabbed the baseball bat, the chances of this guy hitting you goes from 1/3 to nil.
Difficult to Pull Off?: Swing. Wait. Swing. Wait.

Space Harrier 2

Stage 10 Boss

Type: Wut?
Description:
Don't blink.
Difficult to Pull Off?: What happened to the boss?!

Ghouls N' Ghosts

Stage 5 - Sub Boss 2

Type: Exploiting Collision Detection
Description:
First, trigger this pair of sub-bosses by climbing the ladder, then go back down. Trigger the chest and stand on it.
From this position you only have to dodge the odd fireball the right head fires, and when the left head lowers it's head, for what-ever reason, you can hit it through the floor.
This clearly wasn't intentional, as you can't normally fire projectiles through the floor or wall.
You'll have to fight the right head normally, but it makes this section just that little bit easier.
Naturally though, if you brought along either the sword or flame weapon... just kick yourself. You'll never beat the game with those weapons, and you're kinda screwed at this point.
Difficult to Pull Off?: Not really no. It's the safest method of taking one of these things out. Every little helps in this final gauntlet.

Sonic 2

Chemical Plant Boss

Type: "You're too slow!"
Description:
Considering how many people found this boss to be difficult in their childhood, it's amazing to realise that you can easily defeat him before he even attacks!
Jump just slightly before Robotnik appears on the screen, and keep bouncing. Keep a eye on how many times you've hit him, and on the last hit return to the safety of the middle platform.
The Sonic series is full of quick kills for bosses, this is probably the most famous one.
Difficult to Pull Off?: You might mis-time it the first time you try it, but the timing is really easy to remember for future encounters.

Streets of Rage III / Bare Knuckle III

Stage 1 Boss - Shiva

Type: AI Glitch
Description:
Shiva's probably one of the hardest first bosses I've fought in any beat 'em up, ever.
And, out of all the things shown in this video, this is the only one that relies on just a little bit of luck.
Sometimes, Shiva's AI will completely glitch out, and he'll become set on hitting you with a Final Crash.
And he'll keep doing it until he hits you, or you move out of the way. A running attack is the easiest way to knock him out of the Crash move, and he'll attempt it again, and again, and again, repeat until dead.
Very rarely, Shiva's attack will get priority, but if this does happen, hopefully, you'll have dealt enough damage for the battle to nearly be over. Or he could beat the snot out of you. Shiva's a total bad ass like that.
Difficult to Pull Off?: Don't hold your breath on this happening. But when it does happen, take advantage of it.
This screw up can even happen during the rematch at the end of the game.

Golden Axe III

Path A - Stage 2 Boss

Type: This is a boss?
Description:
Take notes guys: Unless you do it in a creative manner, groups of enemies never make for good boss fights, especially when the game allows you to eliminate all minor enemies on screen at once.
Golden Axe simply got around this by not throwing every enemy at you at once (and did it in such a creative manner in stage 4 that I love that boss fight!), and Golden Axe II just gave the group more health than usual.
But Golden Axe III? Naah. Basic enemies. No health increases, and put them all out at once. Clever.
Difficult to Pull Off?: Just keep full magic until you reach this boss. One Hit KO!

Sonic CD

Palmtree Panic Boss

Type: Exploiting Level Design
Description:
You might remember this from my Sonic CD Boss Run. It's a rather funny exploit.
Jumping at the right time and hitting the boss at the right time leaves one very dead boss in seconds.
This doesn't work in the Good Future variation of the level, due to a minor change in the stage design.
Difficult to Pull Off?: If you mistime it, you'll get hit. But you can still hit him from behind. You don't have anything to lose really.

Super Thunder Blade & Other Games Like This

Most Sub-Bosses

Type: Dumb Bullet Pattern
Description:
One problem with games like Space Harrier and Thunder Blade, is that bosses like this can simply be avoided by moving around it circles. This is especially crippling in Thunder Blade, what, with the player having Homing Missiles and all.
This doesn't work on every sub-boss, most notably, the 4th one. You'll have to get a different strategy for that.
Difficult to Pull Off?: Depends on the game. In Space Harrier II, you actually have to aim at the bosses, for example.

Arrow Flash

Final Boss

Type: Most. Retarded. Safespot. Ever.
Description:
I cannot tell if this was intentional on the part of the developers (like in Gradius games), or just a complete lack of playtesting.
By sitting in front of the boss, not only do you cancel out it's attacks, but the few it gets to pull off CANNOT HIT YOU.
This is a perfect example of a dumb boss. Most decent shoot 'em bosses leave safespots where you cannot hit the boss, but it cannot hit you. A stalemate if you will. Gives the player a little breathing room whilst they figure out what to do.
Normally, you have to put yourself in danger to take down the boss. But not Arrow Flash. Oh no. Not it's final boss. You are only safe when you are in front of it's face.
Difficult to Pull Off?: You're kidding right? I don't think this method works too well when using the Mecha form, but I haven't actually tested it.

CONGRATS! You're the 'th person to prove they're intelligent enough to actually READ the video description!
No really, I really do mean this, I'm not trying to patrionise you.
Great stuff. If only there were more of you. Youtube would be a much better place. So be sure to keep it up, you're already head and shoulders above the majority of that website.
Someone actually bothering to read something, it always makes my day.
You'd think it wouldn't be that big a deal, but considering some people on the internet... yeah. It is.