New to Flash AS3, Need help with some weird issues, have .fla link attached...

There are at least two things you're doing wrong. You can't go to a frame where something exists for the first time, and immediately do something to it. Like in your playunit functios for example:

gotoAndStop("unit1")

unit1_mc.alpha = 1

unit1_mc hasn't yet drawn itself on stage to have its alpha set, and so there's an error. That is something that was improved in Flash 10, so if you had set the Flash to publish for Flash 10 and not Flash 9, then the floor plans and the back buttons appears ok. It would sometimes work with double clicks because by the second time you clicked, the movieclip now existed. You might be able to do what you want by having all of the room units on frame 1 of the siteplan_mc, and then set their visible to true or false as you need them, instead of doing the gotoAndStop().

The other problem is that you're trying to set listeners on the Back buttons that don't yet exist. Wait until you're on the frame where the buttons exists, and then set its listener for the mouse click.

Other things you're doing could be improved too, but really you might want to get together with someone who has done more AS3, to help you become more familiar with how it works.