Textmate comes with an Mac OS X input manager so it can be used in all Cocoa applications as an editing app with all goodies textmate has to offer (spellchecking, syntax highlighting just to name two).
All you need to do is describe in detail here.
Not all apps are cocoa, so is Firefox. But there’s a light at the end of the tunnel: It’s all Text! is a firefox plugin that enables Firefox to use any editor of your choice to edit textareas.
A little “hacking” is required for this to work under os x as explained here.