Currently it is recommended that you only have one shortcode form and one widget form per page.
You can put more than one on a page. The problem comes in with the server response to the form submission. Lets say you have four forms on a page, A, B, C and D. If the user submits form D, everything will work correctly. You will get the correct information and the user will get the correct download, but the "Thank you for Registering" message will show up in all the forms. It looks odd and unprofessional.
We recommend only putting one per page, my reasoning is purely SEO. Content is King! It's better to link to each download with content describing that download and a single form.
However it is on the Feature Request list to make this possible.