When I attempt to open Firefox3.5.6 from my desktop I always get this error that states the following:

"Firefox could not install this item because of a failure in Chrome Registration. Please contact the author about this problem."

This error comes on twice then Firefox will open. If I previously had two or more Firefox windows open and closed them out and then tried to reopen them I will get the two errors for each previously opened window that is trying to reopen, ie two Firefox windows will give me four errors and three Firefox window attempting to reopen will give me six errors which I will close by pressing the "OK" button in each error window.

This is very annoying.

Andy

Shouldn't you be checking the FF forums for this issue ...

It would also help if you were to say which OS you were using ...

When I Googled the issue, there were at least 10 different threads ...

Don't you believe in Google ?

Last but not least, get your shortcuts organised (what a mess) ...

Like StevePaul you should of checked the Firefox Forums for this.
But anyways, I did a little research myself on this issue for you.

First of all start Firefox in Safe-Mode.

If it doesn't happen then It is most likely caused my a Extension or Theme. So Start by Turing off your Extensions 1 by one and Restarting chrome after each time. Do the same with your themes. When the problem stops then You will know what is causing it by what ever you turned off last.



If that doesn't work then follow the steps here:
http://kb.mozillazine.org/Standard_diagnostic_-_Firefox



and for your little shortcuts problem, get the free version of this:
http://www.stardock.com/products/fences/index.asp




@StevePaul Try this next time: http://lmgtfy.com/ for all the people that don't know how to use google.