After we had migrated from SharePoint 2007 to SharePoint 2010 we noticed that some document libraries didn't have the Add document" link and the small tick box. The following screen shots show comparison between a working and non-working document library:
Working Document Library:
Non-working Document Library:
At this point, the quick fox was to create a new standard view and make it as the default view. I will try to investigate the issue and update the post.