Checkboxes won't maintain the checked attribute from page to page like that. Did you also expect the add to cart to add items checked on previous pages? That won't happen either.
I could help you get something like that working in a premium support ticket, but it is going to be quite a bit of work. We will have to submit the checkboxes in the navigation and maintain the checked values in the session in an array and then use that stored array to re-check boxes and eventually add to the cart.
The error message is because you have deleted the quantity input field and are just using a checkbox. The solution is probably to just update the quantity to "1" on the line referenced in the error.