After updating to version 10 I closed Firefox.

I noticed that there was a lot of CPU activity.

Checked Task Manager and noticed that in Processes, firefox.exe and plug-in container were running. Opened Firefox and closed again but the processes were still running in TM.

Highlighted firefox.exe in TM and clicked End Process. Both processes disappeared from TM.

Have opened and closed FF a couple of times since with no problem.

However, the OP seems to indicate that this is a problem that re-occurs.

Why is FF not shutting down properly? Is it possibly something to do with the automatic check for add in/extension updates?

Thanks, your answer confirms that this problem has to be temporarily solved in Task Manager, where most people do not want to touch anything....

Sorry, that updater.exe isn't from Firefox itself, something else launched that process.

Firefox checks for add-on updates as it is launched and checks for the availability of an update for Firefox about 5 minutes after launch; neither uses a separate update process, they run from the firefox.exe process.

plugin-container.exe is the only other process that Firefox would spawn or launch - one instance of that process for each file from websites that would use a Firefox plugin.