The most common cause of the multi-file upload field failing to function is the scripts being included down in the footer when they should be up in the header. This usually happens when using the function call to embed the form, there is a second function call you also need to use to ensure the scripts are included correctly: http://www.gravityhelp.com/documentation/page/Embedding_A_Form#Enqueue_Scripts_and_Styles
Gravity Forms 1.5 introduced the gravity_form_enqueue_scripts() function which allows you to easily enqueue the necessary Gravity Forms’ scripts and styles when manually embedding a form. This is also useful if you are using a GF widget and do not wish for the styles and scripts to be loaded inline. https://www.gravityhelp.com/documentation/article/gravity_form_enqueue_scripts/