Sharepoint - How can I force SharePoint 2010 to open PDF's in the browser?

Bad advice! You should not just blindly enable permissive mode.

First of all, there are good reasons why SP2010 does not render files in browser, PDF included, per default. The reason is client object model.

PDF allows for Javascript execution, and though to some degree the threat model is the same as with SP2007, CLient object model makes it a lot easier to create potential malicious code in PDFs.

After considering the possible dangers, you could enable permissive mode, but that would mean that all file types would b enabled. Instead, it is much less of a security hole to just enable pdf as an allowed inline mime type for the web application:

$webapp = Get-SPWebApplication <your webapp url> 
$webapp.AllowedInlineDownloadedMimeTypes.Add(“application/pdf”)
$webapp.Update()

Read a thorough post of the potential dangers here.

This change was made due to security reasons in SharePoint 2010. You know that PDF actually stands for "Potentially Dangerous Files".

You can change it to a less secure mode, per Web Application, in Central Admin. Just change the Browser File Handling property to Permissive and your good to go.

This is controlled by the installation of Acrobat itself, not SharePoint. By default, PDFs open in the browser but many corporate installs force it to open in a separate window for support reasons.

Many users do not realize they are viewing a PDF instead of a web page and get confused when the normal web tools do not work properly. The bigger the corporation, the more likely this is to be the default.