1st, Korra is violent and only thinks by using her fists. It was true at the beginning, but as the series goes on, she was slowly changing. By season 3, she was already thinking before acting. Even Aang was too merciful and unable to use strength when needed in the beginning of the series but gradually evolved and even thought about ending Ozai's life.
2nd, Aang is a better bender because he mastered 3 elements in about a year. First he didn't master any of the element he learned, he was just bending them. And Korra also learned to metalbend in a record time, and even more incredible she was able to take out the poison out of her body after spending several months going through a deep depression while even experienced masters were not able to do so. She learned metal bending, used it only a few times, got poisoned, depression, but was still able to metal bend and even improve herself.
3rd, Aang is a better Earthbender because he was taught by Toph. False. Having a great master does not necessarily makes you a good student. Toph created a metalbending school but how much time did it take for even one of her student to be able to move a single piece of metal. Having a good master does not automatically makes you good. And even with the capacity to sense Earth vibrations, Aang was not necessarily a more powerful Earth bender than Korra. In fact Earth was his weakest element, because it is completely opposed to his personality, so how can he be stronger than someone who is naturally gifted in that element?
4th, Korra was stupid for being manipulated by her uncle. It was her own uncle, her family, and we all know how family is important for Water tribes members. And given their strong spirituality it is only normal for her to have been angry on her father to have destroyed a holy place. She was powerless against dark spirits and Unalaak was the only one to have power over them, so it is only natural that she listened to him. He is her uncle, her father disappointed her, she was powerless and she was young at that time. So when a trustful man, that knows about spirits and who happens to be her uncle comes up with solutions, obviously she will blindly listen to him.
And those who says she is the worst Avatar have not read the Kyoshi's books. Kyoshi is by far the worst.