Apple - How do I stop the "Are you sure you want to open it?" dialog box from displaying when I open an app?

If you need to do this manually on a file (or files) you can run the following command to remove the Quarantine flag:

xattr -d com.apple.quarantine /PATH/TO/FILE(S)

So in your case since the quarantine flag is not being removed you will want to run the command with sudo as the primary cause for the flag not being removed after hitting "Open" is because you don't have permissions to do so.

Create a file called com.apple.DownloadAssessment.plist under Library/Preferences with the following:

<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN"
   "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
  <dict>
    <key>LSRiskCategoryNeutral</key>
    <dict>
      <key>LSRiskCategoryContentTypes</key>
      <array>
        <string>public.item</string>
      </array>
    </dict>
  </dict>
</plist>

Then log out and then log back in.

Instructions for Snow Leopard are a bit different.

Deeper would be a good choice but I would suggest you to use OnyX

OnyX provides a few more features than Deeper, allowing you to verify the Startup Disk and the structure of its System files and to delete caches.