This may or may not have anything to do with it, but....
perhaps the source the link at slackbuilds.org points you to, is for the Slackware 12.2 version?
I say this because, if you were to download Opera 10, from the link on their main page,
it will give you a qt3 version as they don't, yet, show an option for Slackware 13, which runs, I believe, qt4.
You might try going to this page,
and follow the links to the download page for the latest version. I running it and haven't had any problems. The 32 bit version can be found here,
Be sure and download a qt4 version.
I hope that helps.
BTW, these are binary packages. No compiling necessary.
To install, download to whatever directory/folder you like.
Unpack it using, for example,
tar -xvzf opera-10.10-4609.gcc4-qt4.i386.tar.gz
Then "cd" to, opera-10.10-4609.gcc4-qt4.i386
Change to root by running the "su" command and entering your password.
Once done, at the command prompt type, ./install.sh
Say yes to the few questions and you're done.
Exit as root and fire up Opera as user.
Works every time for me.