One of my pet peeves not just with Opera but really any web browser is how poorly they handle unexpected crashes or shutdowns. Chrome and Opera allow you to re-open previously open tabs BUT:
1) If you're on a page using infinite scroll (for example many tumblr.com sites) your position in the infinite scroll is lost. You're kicked back to the top and have to scroll through hundreds of posts to get back to your former position. Depending on how far you scrolled that could take a LONG time. It also requires you remember exactly what post you were last on.
2) If you're entering form data (again think creating a post on tumblr.com, wordpress, blogger, facebook or using some sort of CRM system, or entering your resume into a website) and your browser crashes, you're taken back to the same form but everything you entered into form fields (particularly text boxes) is GONE. You have to re-enter it all again from memory. What a terrible user experience.
Browsers should periodically (say every 1 minute - user configrable) save their current state. Not just what pages are open but every other aspect - position on the page, entered form data, right down to what position was my cursor last in. Let me pick how much state data to keep (the last 60 minutes for example).
When my browser closes either unexpectedly or in a planned way I should be able to open it back up and have the option to pick up exactly where I left off.