(eNotes editors may only answer one question per response. If you need more help, please resubmit other questions separately.)
The immediately obvious remaining problem in the United States in 2081 was that the weather was not as controlled as the lives of the people. "April, for instance, still drove people crazy by not being springtime."
Other problems stemmed in large part from the efforts to ensure that all persons were equal. Hazel, who is "perfectly average" and therefore doesn't need any handicapping devices to bring her mental capacity to the level of equality with everyone else, is curious and a little jealous that she is left out of experiencing the sensations George does. "I'd think it would be real interesting, hearing all the different sounds," said Hazel a little envious.
Apparently some individuals attempt to reduce the load of their handicapping devices through various means. George is not willing to risk the penalty for being caught removing even one piece of birdshot from the bag around his neck. He respects the necessity of enforcing equality, regardless of how heavy it is.
If I tried to get away with it,...then other people'd get away with it-and pretty soon we'd be right back to the dark ages again, with everybody competing against everybody else. You wouldn't like that, would you?
The largest imperfection portrayed in the story is embodied in Harrison himself. As described in the news bulletin, he was a threat to society because it was not possible to reduce him to equality with everyone else. "He is a genius and an athlete, is underhandicapped, and should be regarded as extremely dangerous." Anyone who was so different from the norm would have been considered very threatening to society as a whole. Even if Harrison was an extreme exception, there may have been others who were also underhandicapped, thereby disturbing the equality for which the perfectly equal society was striving.