Escape from Durnholde Keep: More than a few members of the Alliance would probably want Thrall to remain in captivity. Sure, they'd miss his assistance at Mount Hyjal, but they wouldn't have to deal with the greater threat of a cold war with a unified Horde later on. However, it's unlikely that the leaders of the Alliance would want to stop Thrall, because they're mostly smart enough to realize that they may need his help again in the future. Staghelm might be pigheaded and/or racist enough to do it.
If Thrall never escaped from Durnholde, there would be no united Horde. The orcs and the trolls would probably have been hunted to extinction by the Alliance, the tauren would still be nomadic, and the undead would be holed up and surrounded in Undercity. No Horde leaves us with two options: the Burning Legion wins at Mount Hyjal due to Azeroth's lack of forces (see above), or the Alliance wins a narrow victory. Daelin Proudmoore is still alive and the Alliance is totally dominant over Azeroth. This sounds nice, but eventually they'd begin fighting among themselves, plus they'd have to grind twice as hard to open the AQ gates.
Black Morass: This is another one where the Horde would want to preserve the timeline, while some of the Alliance would want it destroyed. Medivh opening the Dark Portal is seen as a bad thing for both sides. But let's think about it. You wipe in the Black Morass and the dragons kill Medivh before he opens the portal. The Shadow Council is stuck on Draenor, but the Council and the Legion are still up for invading. Either the Shadow Council finds another pawn and everything goes as planned, or Kil'jaeden gets frustrated, says screw the plan, gets rid of the orcs and finds a new portaly way to Azeroth directly, this time making sure to leave the night elves until every other race is dead. The human nations never unite and are unprepared for the Legion.
Even if Azeroth managed to beat the Legion, we'd be screwed again at Mount Hyjal. Medivh dying before he was supposed to means he probably wouldn't be redeemed enough to come back as the Prophet, which means no one gets warned about the Burning Legion, which means no one's prepared for the Third War. Oh, and no Horde either.
Old Stratholme: Okay, this is the big tough one. Killing Arthas during Strat would be like killing Hitler in art school. You'd save thousands of lives. But this could go either way. If you killed Arthas, Uther would have lived, the Sunwell wouldn't have been destroyed, Illidan would never have become a demon and probably wouldn't have been asked to serve the Legion, Sylvanas would be alive and happy, and the Lich King would have lost his strength and died without a successor. In fact, if we killed Arthas, both the Scourge and the Illidari would likely be defunct.
However, as noted in the above thread, killing Arthas could upset the whole balance of things. If Arthas is dead, he doesn't tell Illidan about consuming the Skull of Gul'dan, which means that Mal'ganis and Tichondrius are alive at the Battle of Mount Hyjal (assuming someone else summons Archimonde into this world), which means one of the two is likely to alert Archimonde to the wisps being A TRAP!!! As Tarsonis says in the thread, "You could add the entirety of Lordaeron to Azeroth's fighting strength and I'm still taking the Legion in the Third War if Tichondrious lives, because nothing was stopping Archimonde except his own arrogance, which Tich likely could have fixed." Even if killing Arthas stops anyone from being strong enough to summon Archimonde, that just means that Archimonde would still be alive ... and controlling the Scourge after Ner'zhul lost his power. Not fun.
So, it looks like messing up any of the four instances could somehow cause the Burning Legion to win at Mount Hyjal. That might be a big clue as to who's behind the Infinite Dragonflight.
What do you think would happen if you failed in each of the Caverns of Time instances? Do you think that it would be worth it to kill Medivh or Arthas, or would you consider it too risky? What other CoT instances would you like to see?