My newish supervisor has terrible communication skills, resulting in a fair amount of chaos. From my standpoint, better communication would solve many of the current problems. Do I point this out? I don't want to appear adversarial, but the chaos has made a previously pleasant working environment into a stressful one. I think that this person might be too insecure to take such criticisim constructively. How long do you wait out a manager with poor leadership skills?
It's pretty presumptuous of you to think you know exactly what is wrong with someone who outranks you and to think the problem is something so soft as "better communication". Honestly, if you brought that to me (your boss's boss), I'd barely pay attention to you. If you want to make an impact on me, document very specific instances where you think communication would have helped and bring me your solutions. I need to know you actually have something to offer and are not a complainer. Show me specifically how your manager displays poor leadership and please avoid whining about nonsense.