How cloudy it is, quite often is due to crystallization. I just let it crystallize, and put it on the windowsill to encourage it to happen quickly and therefore more smoothly...
The air and the wax, as you saw, will float out or to the top. A piece of saran wrap laid across the top of the honey after it has settled will get the "scum" off the top. I lay this on a plate and skim the honey off for my biscuits... I don't mind some wax...