One reason to dissuade users from using the clipboard to paste passwords is this: the password stays in the clipboard.
Not all users realize this, and so .. don't 'clear' the clipboard after logging in .. which means their password is still available to anyone else who might use that computer.
That seems like an incredibly weak argument: if an attacker has physical access to the machine, all bets are off. How do you know that there wasn't anything installed to MITM everything already?
That's an interesting idea actually. My first response was that you can't freely interact with the clipboard but you can set it provided you do it in response to a js event so in theory that is possible. The only problem is that you'd need to be sure the clipboard did actually contain the password because of course you can't read it. I guess you can log whether onpaste fired and then if the login button is clicked with a second or two, clear the clipboard.
And by 'clear', I mean add a textbox, set its value to an explanatory message '{app} cleared the clipboard because it contained your password' and then execCommand on it.
Hopefully there is nothing important in the clipbkard, like some data that the user will attempt to submit a second time after logging in. It sounded like a good idea at first, but now I want my +1 back :p
I've written short Powershell functions that watch your clipboard and send it over UDP to a remote Powershell session. Does your favorite Powershell module have something similar? It could simply load with Powershell and start logging your clipboard.
Not all users realize this, and so .. don't 'clear' the clipboard after logging in .. which means their password is still available to anyone else who might use that computer.