DOTA is an incredibly difficult ecosystem to balance - there are so many heroes, powers and items - any hero can be overpowered in the right situation...the real key to whether something is OP or not is HOW MANY situations they're very strong in, and how easily/effectively you can counter them.
The other difficulty is the wide range of skills that the game has to fit across - some heroes with ridiculous micro or skill-shots might be overpowered in Pro games...but very ineffective amongst beginners. Some heroes only work well with good team-work and co-ordination from other players. At the end of the day the rules have to be the same for everyone though...
X Hard Carry is overpowered
We've all had those games where
Faceless Void or 
Anti-Mage gets fed, or your team spends the whole time trying to outfarm him and fail massively. It can seem unfair where the likes of Void pops a 
Chronosphere on your head and bashes you to death while you're powerless to defend yourself.This is understandably frustrating...but the real fault lies with your team in allowing him to get enough farm to do that much damage...he's next to useless without it. Same with
Anti-Mage - he can seem OP when you just can't gank him and he ends up dominating the game - again though, you probably didn't pick or make the right counters, or have the right tactics.Is Nyx OP? (54% win rate, 22nd most popular)
Nyx Assassin has been getting a lot of playtime recently as people have cottoned on to how to play him successfully. He's got a lot of ganking potential, and while lacking the right click damage of say 
Clinkz or 
Riki, he has a lot more survivability, plus a lot of burst damage.Personally my issue with Nyx isn't so much with
Spiked Carapace (although it is VERY strong), but with 
Mana Burn. It's just devastating in lane if you're using an Intelligence hero. At 90 mana it's cheap and there's no way of avoiding it other than to the leave the lane or hide.So is Nyx OP? Well, I don't like to rush to judgement on these things...certainly it can be argued that he's a strong hero at the moment, and that you maybe need to consider your lanes very carefully when he's playing - strength heroes won't have the same issues with him at all.
Is Drow OP? (Win Rate this month 57%, 1st most popular)
There's been even more people complaining
Drow Ranger is OP since her recent makeover. She used to be a devastating late game carry, but now she seems much more dangerous while laning, and doesn't disappear mid-game. Is this a case of she was already pretty strong and the remake just made people notice? Or was the remake fundamental?I think part of the issue is that she's got a very straight forward playstyle - this means it requires less teamwork and skill to use her effectively than it would for other heroes. This can allow her to be very effective in lower end pub games especially.
Troll Warlord (Win Rate 51%, 97th most popular - early days thou)
As a non-DOTA 1 player I don't know much about new heroes when they appear other than what I get the chance to read up on them. Troll certainly is an interesting new addition, and it takes some time to figure out how best to counter or help him. The big discussion at the moment seems to be around his ultimate
Battle Trance. Being able to blast out that much extra attack speed, for your whole team, for approx half the time in the late game is very much up for debate...Interested to hear people's thoughts below the line!
I have never noticed Nyx being that strong, but I never had to lane against him with any int hero.
As for Troll Warlord, I hate him, so when I can (almost every other game) I lane against him. And he is not this "big deal". If he can feed it is the same as above, but otherwise he goes down like any other hero, as being really squishy in early laning stage. His ulti on the other hand it's really nasty: +180 IAS mean nearly +200% attack rate if I'm not wrong. For his whole team. Everywhere. Everytime. But still I dont find it gamebreaking (altough I would like to see it tweaked more reasonably), it usually happens that the team retreat for thoses 10s and then we start the real teamfight. Also pubs's Warlords seem to be selfish and the ulti start only when they need, no matter if the teams are fighting already.
Ps: all my thoughts come only from pubs and reading about, I'm no authority over such arguments.
However, phantom lancer and alchemist can be said quite power, they both has a skill to owning on early game, and skill for farming.
And Troll Warlord as well as Drow Ranger is a joke, nobody use them actually unless for fun game and maybe serious game for noob.