I've had no problem running 2011 ink. If it is sealed when you open it. I had only one issue with a Light Black, but it was a known problem with the chip on it, not the ink.
Use the ink until the printer stops printing. There will still be a lot of ink in the cart. I'm not a fan of using carts which are not sealed or have previously been in a printer. Any evaporation can change the viscosity of the ink. Plus, i don't know how contact with air "oxidizes" the pigments?