Indomitable Will: The Joker's insanity, or his frame of mind, made him immune to the Spectre's judgement, though warranted. Batman once explained that the Joker doesn't actually know what was right and wrong, a crucial understanding the Spectre needed to judge. In a way, one had to know one's deeds are evil or wrong for the Spectre to judge, and the Joker doesn't. Also, both Jim Corrigan and Hal Jordan's Spectre have had major problems with navigating the Joker's mind, Corrigan even managed to get lost in it and Jordan literally was blasted out of his boots to the moon when he tried.
Genius Level Intellect: The Joker was highly intelligent and skilled in the fields of chemistry and engineering, as well an expert with explosives. He was capable of hijacking television and radio broadcasts.
Gadgetry: The Joker commits crimes with countless "comedic" weapons such as; razor-sharp playing cards, acid-spewing flowers, cyanide pies, lethally electric joy buzzers and his signature Joker venom.
Hand-to-Hand Combat (Basic): The Joker was moderately skilled in hand to hand combat. Although Batman was stronger, the Joker was faster and more agile, and his fighting style was chaotic and difficult to predict. The Joker had been known to be able to hold his own in hand-to-hand combat against Batman, however every time he was subdued it was through physical force. However, the Joker has proven to be very skilled in the area of martial arts as well, this being proven when beating the Batman once in a fight without "cheating".
Intimidation: Joker was adept at torturing his victims endlessly, including shooting Batgirl, torturing Robin to death and beating Damian into submission.