Typically, this is caused by incorrect formatting of the PDF file name. The name of the file itself should not contain any spaces or special characters because it is included in the URL that is generated by the CMS File Library.

A PDF file titled "Test Document" (containing a space) will have a URL created similar to the following: http://www.blackbaud.com/folder/test document.PDF
This link will not work in a web browser.
Instead, rename the file "Test_Document" (no spaces) and re-upload to the File Library.
This will generate a URL similar to the following: http://www.blackbaud.com/folder/test_document.PDF
This URL should work correctly.