Heath Ledger's Joker is indeed a good character in how accurately he captures the core traits of a psychopath better than any other movie villain (something backed up by reviews from actual psychologists, no less). His lack of real allegiance and embracing of chaos in order to prove a point to Batman are extremely well done as well as his analysis on the core evil within human nature and the need to survive. Whilst his insanity is portrayed well, it also means that some elements of him are overly inconsistent such as him giving contradicting stories about his backstory. This indeed fits with his personality and isn't a bad thing as inconsistent insanity is with many characters, but does avoid having a solid foundation for his character arc. Speaking of which, therein lies one thing that holds this incarnation of the Joker back in that he doesn't really have much of a character arc beyond bringing a few of the film's themes to the forefront and being a direct opposition to Batman and beyond being captured, his arc at the end of the film has no catharsis due to being so open ended.
Also, his plan to have either Rachael or Harvey killed relied on way too many variables to be pulled off 100% perfectly such as knowing precisely when the police would discover Dent was missing, when and for how long Batman's interrogation would commence and have all that culminate in Batman only having a few moments to save just one of them. This would make sense in his maniacal nature meaning the plan wouldn't be foolproof, but the fact everything went according to plan comes off as way too much of a major plot convenience. This overall damages his character somewhat due to it neither fitting well within the insane element of his personality or complete strategic genius.
Heath Ledger's Joker would be a 10/10 if I were rating him purely on acting performance. That isn't the case though and despite being the perfect conveyor of the film's initial theme of humanity's madness, he lacks enough of a solid character arc or consistency to really be a perfect character. The version of him from The Killing Joke is arguably better due to having far more of a solid backstory and his plan not being so over the top as to have massive holes within it.
7.5/10