In my site previously there was a drop down list to select product custom options , now I implement a jQuery ui slider to select product options in a product page. But I am getting error "Please specify the product required option(s)." while I am clicking on Add to Cart button. I think custom options are not passing through request.
Here is a image of slider
The problem caused by you only add jQuery UI but you have not add value via form field. You need to catch event change of jQuery UI and set value for form field to resolve this bug.
Hope you success!