Since we made the move to SharePoint 2010, we had some issues (both technical and functional) with the implementation. One of those issues was that our PDF documents could not open in a webpage. We just got the option to save the document, but not open it!
The culprit is the way SharePoint 2010 does the browser file handling. It is a setting that is set per web app.
Solution: Go to central administration – Web Application Settings. Select the web app you want to change, and click General Settings. Scroll down to the Browser File Handling block and change the setting from Strict to Permissive.
This should do the trick. If you have more web apps, you could change it via PowerShell like Todd shows on his blog.