Dear oper support I'd suggest you look at the posting on the microsoft forums.
BUT In summary this is the issue.
Something the Opera latest installer has done has made Windows point the IE app engine calls, to point to Opera.
A symptom of this is seen if you have Carbonite Installed on your system.
Carbonite uses the IE App engine for its interface when Carbonite starts it calls the IE app engine
So if you install Opera when Carbonite launches it calls the IE app engine, as Opera appears to have made itself the host of the IE App engine it launches Opera and three or four Speed dial tabs. (the number of tabs I believe as Carbonite is looking for the IE Engine and tries a few times triggering extra TABs)
If you uninstall Opera, whatever it did to make itself the location of the IE App Engine is not reversed.
So when Carbonite launches at startup (it tries 4 times in my case) displays the errors then eventually finds the correct IE App engine and starts.
Technically any program that uses the IE App engine would cause this issue. I've seen some posts of other applications thats use the IE App system triggering this issue.
So I'd agree it's not a Carbonite issue, carbonite is a symptom of some bad coding on Opera's installer / uninstaller.
Sorry Opera guys you broke it - you need to fix it!!