These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Base Breaker: Deny. Either part of the metagame that people should do, or a Scrappy Mechanic that encourages the "Make the game as unfair as possible for the other team" mentality.
There are *lots* of mechanics that fit into this category, usually mechanics similar to denials that were either bugs, or unintentional side-effects of the Warcraft 3 engine. Most of them are kept in because the devs and lots of players believe it adds skill, but many still believe they're arbitrary.
Catharsis Factor: Got trashed in a legit match? Start a single-player game in a bot-available version, select the heroes that just kicked your (team's) ass, turn on God Mode and kick THEIR asses.
Complacent Gaming Syndrome: To the point where some skilled DotA: Allstars players have some degree of difficulty playing in Ladder.
This◊ picture best illustrates this phenomenon within DotA: All-stars itself. (NSFW)
This one too, if you can understand it. http://www.youtube.com/watch?v=UGlJICZ35ks&fmt=18note Rough Translation: (C)What the hell is that, do you love me less than DotA?/Every night when I'm asleep you're just right here in my arms./When I woke up in the morning, you're not already there./Please tell me the truth, do you love DotA more than me?//When I wake up in the mornin',Gotta play all day in DotA/No money don't no matter cuz I'm ready for battle/I'm dreamin'/to get one off yo dawg/You place the bet dawg gotta beat the opposition/4 on 4 or 5 or 5 that shit will never matter, you will lose motherfucker/I am a farmer, and I'm a killer! Good game now/Play again tomorrow!.//(back to C)//1-2-3, my Mirana's gonna push/She's unstoppable now with my Manta Style/Firing Arrow!/Bang you go again/Damn motherfucker/you're dead once again bitch/Now getting chased, it's got the Leap, boy/Never gonna catch it even if it's Faceless Void/Using TP now/Dream on dawgs/Yeah, son of a bitch I'm gonna get ya back!//(back to C)//(Guy)There's no need to get jealous now/I'll never ditch you off for a game called DotA/(Girl)What kind of fun do you get from that?/(Guy)It never concerns you, just go back to sleep now.//(back to C)
It's actually a song about how someone loves DotA more than his significant other.
Game Breaker: Item pooling. Recently nerfed. Also backdooring (no, not THAT backdooring) and cutting off your opponent's supply of creeps (the latter is debatable). The Fun Tavern (only available in versions where you can team up with and battle the AI) reveals that some heroes of past versions were even more broken.
Backdooring was never a gamebreaker. People just didn't like it.
A lot of items can be game breakers if you manage to get them early enough in the game before everyone else is buff enough to handle them; some particularly nasty examples are the Armlet of Mordiggian, Diffusal Blade, Guinsoo's Scythe of Vyse, and the newly buffed Agahnim's Scepter.
And, historically, a number of heroes have been this, due to the honest mistake of being overpowered when they were introduced. For example, the Moon Rider (whose Beam Spam has already been described) and the Sand King (who, come to think of it, can still stun you / slow you / shove his tail up your bum for the win, just not as quickly), but undoubtedly there have been others both before and since.
Also just recently, the Tauren Chieftain and the Batrider with Radiance... and a little before that, Kunkka.
Phantom Lancer, or as most people call him "Phantom Cancer" is a hard carry that only needs 4000 gold to be end game, can push all 3 lanes without risking his own life, oh and did we mention he has a great early game escape thanks to doppelwalk, which doesn't even clue people in to the fact that he switched places with a fake until the illusion dies?
Griefer: DotA has a terrible problem with people who leave the game. It's slightly nullified in that if someone leaves, the game is declared unfair and lets other players leave without penalty, but this usually just makes the situation for a losing team worse.
Paranoia Fuel: The Night Stalker's story indicates that he is supposed to inspire this in others. On the meta level, a good ganking team can make the other side afraid to leave their base for fear of death, allowing the carry to farm in peace.
Of particular note is the Stealth Assassin. Have sharp eyes, because he has an Invisibility Cloak and more often than not can Back Stab you to death in under three seconds (So does any other hero with an invisibility ability).
Miss mid/nh nh nh nh nh nh nh nh nh nh...
Scrappy Mechanic: Same Hero, Only Mid, and the server chooses Lord of Olympia / Warlock / Goblin Techies. What fun.
Also add All Random and No Powerups, among others. The former is usually only played with friends; anyone playing the latter is "automatically" a Scrub.
What happens if someone leaves? They trash the whole game.
Scrub: Most players starting out play like this: either their attitude improves or they get worse.
Usually they get worse first, due to finding some league/tournament rules, afterwards some of them get the attitude improvement.
Suffers Newbies Poorly: Both in terms of the gameplay AND the player base. It doesn't help that if you play poorly, you will bring your team down by giving lots of gold and XP to your foes. If you do, expect cries of 'noob' and people demanding you to kill yourself.
They Changed It, Now It Sucks: (Almost) Anytime a remake of a skill or hero occurs, even one that allows the "victim" to become competitively viable, someone somewhere will cry foul.
There's still some noise being made over Valve's remake as well.