quick analysis (and some of my opinion) of stage counterpick groups:
Counter Pick Group One
Typically used as CPs, don't really have to go over this.
Counter Pick Group Two
These stages aren't legal everywhere but mostly are fine in that A) they provide consistency in results and B) there are no dominating stage strategies.
Pictochat:
Two main issues of the stage are randomness and stage hazards. There is no set order in which stage transformations appear, and some of the stage hazards (missles, cart, spikes from the bottom, spikes from the sides) can kill or at least influence gameplay. Overall though none of the stage transformations are too "broken". The cart is the only transformation that can kill and reasonably come into play (in the spikes transformation it's generally a bad idea to approach, but you can get u-throw or u-whatever kills from the cart). The missiles don't kill but do a set amount of damage. Despite the randomness, the stage usually provides consistent results and none of the hazards bar the cart do more than already existing ones (like on halberd or brinstar).
Rainbow Cruise:
I don't see the problem here and it's been legal like everywhere.
Pokemon Stadium 2:
The two "issues" are a change of physics and Marth's Dancing Blade glitch. The change of physics overall isn't a problem (IMO) and they don't last long. On the air transformation, don't jump vs. MK. On the ice one, everyone has increased traction (except maybe Ice Climbers although i might be completely wrong i only heard this as a rumor lol), which doesn't create any broken strategies in actual gameplay. The electric transformation doesn't pose any broken strategies either, although there's a glitch where if Marth uses dancing blade at the end of it (or maybe it's the ice one) he just goes flying off the screen and dies. For all of the other characters this is a fine CP (IMO).
Jungle Japes:
I don't think there's a definite "problem" on this stage aside from the klaptrap, but I just know Falco's really good here lol. The klaptrap comes every 10 seconds, and you can't land in the water to the left of the left most platform. Anywhere else, you'll be able to recover (even Oli with no Pikmin can recover just to the right of the left edge) but you can't spam jump, you have to time it.
Norfair:
The lava and possibly camping are "issues" here (I don't know too much about the stage to be honest lol). This stage is legal some places (maybe half). While the lava is avoidable if you're playing by yourself, in a match it will come to play. Some people find that it's not too intrusive, others think it is too intrusive.
Counter Pick Group 3
These stages are....eh. Each has plenty of "problems" and often on each stage zoning is a much more present factor in 1v1s than PvP factors are.
Green Greens
The two main problems are the bombs and apples (and the camera wtf). The bomb blocks spawn randomly, and the apples can spawn randomly as projectiles, food, or bombs. To be completely safe from the bombs, you have to do predictable things when passing over them (like jumping over and airdodging), and maybe it's just me but the camera's always wonky and I don't always see the bombs. This isn't a stage I know too much about tbh, but from what I've seen it doesn't always provide consistent results due to the bombs. Most people have a preference against it though.
Distant Planet
Main problems with this stage are a light circle, walkoff camping (and walkoff CGs), and very powerful stage positions.
-From the right edge to the bottom of the slope there's a light circle you can abuse to run away. Projectiles do spawn on the stage and they can help you combat this, but this is still a problem.
-The bottom of the slope is an ideal position to be in for a lot of characters, the best being MK. He's in an ideal position there because he can shark the main stage to the right and force you to approach down on him (which is the worst position to approach against him and most characters). Not many matches are played here trying to abuse all of the stage tactics, so as of now there's no way to know how "broken' it really is (this goes for a lot of the things on this stage actually).
-Some characters (Pikachu being the best but including Yoshi, Falco, others) can CG up the walk-off, and in general walk-off camping can be a problem (due to the walkoff always being there).
On paper this stage is pretty bad, but without many matches played on it it's hard to tell what works and what's just theorycraft. Overall, most people have a preference against this stage and it's hardly legal anywhere.
Luigi's Mansion
IMO this is the "worst" stage on this list (aside from maybe Pirate Ship). There are a number of problems with it, but the main thing is that you're either abusing a part of the stage, destroying the stage so your opponent can't abuse it, or waiting 20 seconds for the stage to respawn so you can abuse it again. If you aren't doing this, you're losing.
Overall though, not only is there a "cave of life" as well as a light circle, but many characters (namely MK and Olimar) have strategies using the bottom ceiling that equate to "free" damage. MK has tornado, Olimar has U-smash tricks (and a small distance top to bottom to approach him, giving him more of a boost). Ultimately, you have to destroy the stage to avoid these things, and the stage is only completely destroyed for 20 seconds before it's rebuilt (which is plenty of time to run away until you get a natural stage advantage).
The problem people see with this stage is that stage zoning becomes more important than most player vs player aspects of the game. I'm not nearly as worried about reading opponent habits and zoning against my opponent's character as I am making sure I'm in a spot to get 30% or making sure I destroy the stage so my opponent can't do that. This combined with a light circle and cave of life effect makes many people dislike the stage, and it's not legal in many places if any. However, this stage was legal for 2008-summer of 09 in Midwest and Texas for sure (as well as other regions probably), so it's not just theorycraft like Distant Planet — people have played and tested this stage already and as an overall consensus banned it.
Pirate Ship
The two main problems are rudder camping and water camping in general, I don't want to get too much into this though. Overall I think it should be banned though, as not only does rudder camping not constitute as stalling except for against some of the cast, but TL's and G&Ws water camping are also very advantageous positions they get from the stage.
Port Town Aero Drive
It has similar problems as Luigi's Mansion in that stage zoning takes more of an effect than other PvP elements. I think the biggest problem isn't the cars (although they are an issue—while they're perfectly avoidable they can come into play, kill at 60%, and port priority determines who dies from the cars in a grab lol) but the edge. Lack of ledge + a track that bounces you back up means that you're taking 50% when you're trying to recover. Many character's recovery options are severely reduced without a ledge.
Another problem is that the stage is inconsistent; sometimes the track will be there and sometimes it won't be and you'll die. In a way this provides inconsistent results.
The possibility of cars on some stops interrupts gameplay, and the lack of ledges + the track that bounces you makes you get punished severely when trying to recover. Otherwise, standard PvP elements occur. I think it's better than Mansion because of that, however many people think that being punished that hard for recovering and stage zoning on the moving platform being so important (because you don't want to be near the edge obviously) warrants a ban.
Yoshi's Island: Melee
I honestly don't know much about the stage and haven't seen it used in competitive matches at all. DMG brought up the problems of potential walk-off camping, walk-off CGs (with like Pikachu and Yoshi's), shenanigans with the slopes, and G&Ws/Marth's planking being an issue in the center pit. This stage generally isn't legal anywhere mostly because of preference, but it has the potential to have quite a bit of issues.
In my opinion, Counter Pick groups 1 and 2 should be legal while 3 should be banned. I can see why those group 3 stages are in that counterpick category and not banned, however I think that stage zoning shouldn't take importance over other PvP things in stages, and that seems to be the case with most group 3 stages. Some people disagree and are fine with heavy stage zoning elements, which is perfectly fine.
i dunno why i wrote all that lol