In Media Library, after clicking on the Attach button in a media item, and clicking Browse, the file dialog does not open.
Until Sitecore comes out with an official fix, you can force “Upload.Classic” mode which will work as intended.
The config setting is
<setting name="Upload.Classic" value="true" />
To avoid messing up your nice, fresh, and new web.config, you could override this setting by dropping a patch .config file in your /app_config/includes directory.
Full file download available on my GitHub here:
Sitecore v7.1 rev 130926