Just installed Chromium Browser (ver. 22, ubuntu package) in Mint 14 Cinnamon 32-bit. Crhomium does not pick up the current system theme properly (see the green tab strip and the scrollbar arrrow). "Use System Title Bar and Borders" menu item is on.
I've just played a little with GTK+ themes. Chromium picks up the correct tab strip color from Adwaita theme, but there is still problems with scrollbar arrows. Seems like the problem is in Mint-X GTK+ theme.