You should already be able to copy multiple rows and paste to spreadsheet.
Also you can try the beta export feature (enable it from preferences->beta features), and you can export high level summary to a csv or html file.
It doesn't have any UI for Copy / Paste (not even context menus), but you can use keyboard hotkeys. Focus a panel, then press Ctrl+A to select all lines in the panel, and then Ctrl+C to copy.
Maybe this could be a little more intuitive, as I didn't discover this straight away, either. A "Copy All" button, next to the "Expand/Collapse All" one, wouldn't hurt.
If you want the stats data, use the File / Export feature to create an interactive HTML+JS file with that info
(it must be first enabled in Edit / Preferences / Beta Features).
You can also save the whole session as a *.flm file (only openable in Scout), but it can take a lot of space, especially if you enable Stage3D Recording.