One of your installed extensions is probably causing the Error Console to open automatically. If you have the Web Developer extension installed, you need to un-check the preference for that action. If you don't have the Web Developer extension installed, you'll need to troubleshoot your extensions to find out which one is causing that to happen.

http://support.mozilla.com/en-US/kb/troubleshooting+extensions+and+themes

Thank you for this quick reply. I don't have the Web Developer extension installed.

I will try disabling several different extensions to determine if any are the problem. Hopefully someone else will have the same odd problem and respond in this forum.

Thanks again!

The Web Developer extension is the most common cause of that problem based upon use feedback here, that's why I mentioned that one specifically. It would be helpful if you gave us a list of your installed extensions, so other people don't come up with more WAG's (wild @ss guesses) like I did .
Help > Troubleshooting information > Copy to clipboard - then paste that listing into a text editor and delete the information above and below the actual information about your installed extensions. Then paste that info into the Reply box in this thread. (That information get's formatted properly when it is placed in the More Information box when you start with "Ask a new question". It doesn't format well when put in a Reply posting.)