According to About.com, the main weaknesses of Ares in Greek mythology were his impulsiveness and bloodthirsty nature . Moreover, he often started fights regardless of consequences.
GreekGods.info discusses that one weakness of Ares was his affair with Aphrodite, wife of Hephaestus. Stories say that Hephaestus caught him in the act with Aphrodite and captured them in a magical net, which held them together as lovers. Hephaestus then presented them before the gods to account for their actions. Ares had a daughter, Harmonia, with Aphrodite He was temporarily banished from Mount Olympus as punishment for his indiscretion.
According to the Ancient History Encyclopedia, in Homer’s version of the Trojan War in the "Iliad," Ares was shown in a less favorable light and described as “the curse of men,” “the war-glutton,” “the man-killer” and the “hateful Ares.” Homer portrayed Ares’ weaknesses in comparison to the other gods. Ares was completely beaten by Athena, who, in support of the Achaeans, knocked him out with a large rock. He was also injured with a spear by the Achaean hero Diomedes. Cartwright notes that Ares was likely the most unpopular among the Olympian gods because of his aggressiveness, quick temper and insatiable thirst for conflict. In contrast to Athena, who used strategic elements in warfare, Ares represented a bloodier and more brutal side of battle.