Stumped on this

In my version you don't need to click things twice. And I added white lines. You *need* white lines as much as you need indenting. Having no white lines is like reading a line of text which has no commas.

Remember this line: You only need a Waitevent() command once, in your main loop from which you call all your functions.
You don't need it in any other fuctions, unless they're self-contained popup things like a color chooser, but you're far from that stage at this moment.

So, you had Select Waitevent() in your functions, that was the cause of your double-click bug, why check again for events? You'd already done so in your mainloop. The waitevent() command doesn't need to be anywhere in your functions because it's not relevant having it there. Waitevent waits for an event, once that event has occured, some global variables are filled, these global variables are (actually they're presented as functions, but nevermind) EventSource(), EventID(), EventX(), EventY(), EventData() and perhaps some more, dunno, read the manual I'd say. :P

So, once they've been filled you can just read them out in any function, no need for extra WaitEvent commands.

Here's an improved version, regarding functionality and readability.

;Event List 
KEY_DOWN=$101 ;A key was pressed down-needs the keys scancode for EventData().
KEY_UP=$102 ;A key has been released on the keyboard-needs the keys scancode for EventData().
KEY_USED=$103 ;A key has been typed-needs keys ascii value.
MOUSE_BUTTON_DOWN=$201 ;self explanatory, needs one of the following values(1=left,2=middle,3=right).
MOUSE_OVER_CANVAS=$203 ;self explanatory, you need to use EventX() and EventY() along with the canvas handle.
GADGET_USED=$401 ;self explanatory, you need to be specific to what kind of gadget it is, and what the gadgets handle is as well.
MENU_SELECTED=$1001 ;something has been selected from a menu, needs the menu identifier
X_HIT=$803 ;The X was hit
APPLICATION_HALTED=$2001 ;Self explanatory, means that the program was suspended
APPLICATION_RESUMED=$2002 ;Self explanatory, means that the program was resumed

window=CreateWindow("UNTILTLED TEST",300,300,400,400,window,15)

uno=CreateButton("1",35,35,35,35,window,1)
dos=CreateButton("2",70,70,70,70,window,1)

menu=WindowMenu(window)
	file=CreateMenu("File",1,menu)
	finish=CreateMenu("End",2,file)
UpdateWindowMenu(window)

guibank=CreateBank(120)
	
PokeInt guibank,0,window
PokeInt guibank,4,uno
PokeInt guibank,8,dos
PokeInt guibank,12,file
PokeInt guibank,16,finish

Repeat
	WaitEvent() ; <- fixed
	Buttonz guibank 
Until EventID()=$803 ; <- fixed

Notify("Ending...")
End
 
Function Buttonz(guibank)

	window=PeekInt(guibank,0)
	uno=PeekInt(guibank,4)
	dos=PeekInt(guibank,8)
	
	Select EventID() ; <- fixed
		Case $401
			If EventSource()=uno Then ; fixed some here and below
				Notify "UNO" 
			ElseIf EventSource()=dos Then 
				Notify "DOS"
			EndIf
	End Select
	
End Function 

Function Menuz(guibank)

	file=PeekInt(guibank,12)
	finish=PeekInt(guibank,16)
	
	Select EventID() ; <- fixed
		Case $1001
			If EventSource()=finish Then
				Notify("See ya!")
				Delay 500
				End
			EndIf
	End Select
	
End Function