Tsunade and here's my reasons:
-She allows Sasuke to roam free for 2 years and now look at him.
-Lets Naruto do whatever he wants,she spoils the boy too much
-All that healing her and the giant slug did was useless since Nagato revived all the dead people anyway(sort of a troll for her).
-She was unable to stop the threat that ws attacking the village(Minato,Hashi,Tobirama and Hiruzen saved the village from being attacked or during the attack the enemy's plans was foiled).
I agree, a Kage needs to represent power, being an unquestioble authority and inspire fear in other villages. Tsunade fails miserably to do so.
(dis)Honorable mentions:
*Hiruzen: didn't really solved any problem. He let escape Orochimaru and couldn't stop the Uchiha coup d'etat without resorting to kill them. Also, for a pacifist he took part in two SWW and invaded Amekagure.
*Hashirama: bad leader, he doesn't inspire his clansmen let alone the enemy. Too soft with a treacherous psycho. His niceness takes the better part of him --> you can't be a leader that way.
*Danzo: I'm mentioning him just because some people are too damn fanboyist. He is not even a kage, he wasn't elected by the Jonins. He was discovered using Shisui's eye = screwed all diplomacy and instantly make a fak every decision that benefited him. He didn't do **** against Oro's invasion (he was a traitor at that moment), exterminated the Uchiha in order to take their eyes and didn't do **** against Pain's invasion.
Worst of the worst, he even surpasses Obito (atleast he is crazy as a goat).