I've had this bug pop up before with Firefox wherein my .swf files that contain text input fields, when typing the cursor stays in one place and only last letter I typed appears.
Anybody familiar with this and know what's causing it or how I can avoid it?
Have you tried disabling any add-ons you have loaded in Firefox?
Is there any chance there's a java applet running in the browser? There's an issue with older versions of the java plugin for firefox that causes text input/cursor issues. I've only seen if affect text input boxes in HTML or in the firefox UI itself, but it's possible it could affect SWFs as well.
That's the only time I've seen something like what you're describing.
i encountered various problems with input fields when your swf is set to wmode=transparent/opaque, see also the this post (in german, sorry)