Type the first character of your password; as a proper password field, it shows *.
Click the little eye at the right of that field
Type the next character (does not have to be correct). Use backspace and a dropdown shows which reveals the complete password.
Tested on
Win7 64 bit with Firefox 53.0.3 (32 bit)
Android 6.0.0 with Chrome 58.0.3029.83
Type a character in the password input field to make the eye icon appear.
Click the eye icon on the password input to turn password obfuscation off (signified by eye with line through it).
Sign in. This will put the password in your autocomplete history.
Sign off
Go to the Sign in page.
Type any character in the password input field to make the eye icon appear.
Click the eye icon on the password input to turn password obfuscation off (signified by eye with line through it).
Delete the character you entered in the password input field.
Press the down arrow on your keyboard. A dropdown appears with the password you entered on the first login.
They need to set the autocomplete attribute for the password input to off. I saw that once before on the credit card input on an online store coded by an amateur but this is the first I've seen it on a password input.
You need to do one login with password obfuscation turned off in order for the password to be recorded in the browser's autocomplete history. If you have only ever logged in with password obfuscation on then the issue doesn't occur because the browser doesn't store the password in the autocomplete history when it's obfuscated. After that first time logging in with password obfuscation turned off it's in the history and you can reproduce the issue by only following the second half of my instructions from then onwards, it is not necessary to repeat the first part of the instructions every time.
I believe this was the reason that ballscrewbob was unable to reproduce the issue at first as I had that problem trying to reproduce it.