Is this a <select> control or a different kind of pull down? It would be helpful if you have a live page or demo/test case to provide a link to it. If you don't have a public one currently, you might be able to build one using http://jsfiddle.net/.

Start Firefox in Safe Mode {web Link} by holding down the <Shift>
(Mac Options) key, and then starting Firefox. Is the problem still there?

The type of pulldown I'm talking about is as shown in the attached image

Typically found in request filters, parameter entry or security screens

I'm not 100% sure but I think it only happens if there is no default or initial value already populated. Only the very first entry on entering the page is affected like this

Does the same thing in "safe" mode

Is this on just one site, several, all? What site(s)?

Verify Java and Find Out-of-Date Versions {web link}

Version 8 Update 40

I have detected it on 3 sites I use

These are all connected with security questions or password entry and of the form "Enter the nth character of your password" from a drop down list with no default set up

The sites are all Financial services companies

Perhaps there is a common piece of code that isn't working as expected on those sites.

Does your Firefox work on a simple demo like this: http://jsfiddle.net/kjbnckqL/