I just re-installed Firefox, but the thumbnail is not showing in the dock applications folder. The icon DOES show both in dock and in finder.
I have tried to re-install Firefox again but without success.
This is a result of one of OS X's security features.
This icon is shown to tell you that the program is potentially unsafe because you haven't opened it yet and it was downloaded from the Internet.
The first time you open the app, you'll see a security dialog that says, "App Name" is an application which was downloaded from the Internet. Are you sure you want to open it?"
Once you click Open on that dialog, the app will open and the icon will change to the app's normal icon.
Usually, you shouldn't need to restart or anything like that.
Since it's appearing on the Finder but not in the Dock, you can force the Dock to refresh its icons by relaunching it: open Activity Monitor, find the Dock process, and click Quit Process.
Mostly copied from my answer on Ask Different