Yup, I did. My tests along with reading through the Zen Cart code is why it really does not make sense... I even tried guest vs. logged into an account (clean Zen Cart 1.5.x and clean Zen Cart 1.5.1 w/ USU)... Not saying you are not seeing the issue in your installation (you would not be here if you were not)... Just saying I have not yet been able to duplicate the behavior...
Had to ask, sometimes the "automated" install scripts bork things. What is the OS of the local computer?
Link to the "test" site so we can see the generated HTML (and form fields - one per each "add to cart")? Any chance the form is being clicked upon before the browser finishes loading and rendering the HTML (such as on a slower server / connection)?
Can you check and make sure the browser is set to not "save" form data? ($_POST is populated from a form... Maybe something in the browser is repopulating the form data with old data? Try running the browser with all add-on's disabled?)
This means you are definitely going to want to check what data is being embedded in the forms (in particular the hidden products_id input field). The generated form + content comes from Zen Cart's core code unless a theme or module has been installed which overrides the code. The same is true for the code handling when "action=add_product" is one of the query parameters in a URL...