This is a really annoying problem. You can see on the next screenshot what I'm talking about.
Why SharePoint just can't download the file and open it? It's the PDF file so you can't edit it anyway.
To be honest, we can't blame SharePoint in this situation. The SharePoint starts to treat PDF files this way after you install PDF iFilter and modify docIcon.xml file in C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\14\TEMPLATE\XML folder.
In this article by Microsoft you can find that when installing PDF iFilter you need to add <Mapping Key="pdf" Value="pdf16.gif" /> entry to docIcon.xml file. The entry should be <Mapping Key="pdf" Value="pdf16.gif" OpenControl="" />. After you update the entry and restart IIS using iisreset, everything should be OK:
Hope this helps,