What situations/political problems are we still dealing with today? Has anything that Heller writes about been resolved?
One situation is corporations and their influence on politics. Imagine is Milo was able to claim his corporation as a person as Citizens United Supreme Court Case said they are as far as political contributions? Heller satirizes the way Milo uses shares that don't really amount to anything, the same way Enron bought and sold from is subsidiaries in order to make profits. The only real money coming in was from investors.
There is also the theme of paranoia which Yossarian is a considerable vehicle for it. After 9/11 the use or paranoia, a "them or us" attitude is being used, topically about the gun debate, where the government is about to take your guns if any gun control legislation is enacted.
As to what has been resolved: there is still a fair amount that Heller wrote about that has not changed. People are still able to manipulate the system no matter the checks placed in their way. Humans are too inventive to really be stopped.