The strange shake issue with the Panasonic's 12-35mm f2.8 lens has annoyed quite a few of us. In a nutshell, when you put a camera with the 12-35mm lens on a tripod and angle it down a few degrees, the image would shake. Very subtle, but unacceptable as it would render the lens useless for certain applications where precision is crucial. The shake would appear regardless of whether O.I.S. would be on or off.
On May 14, 2013 Panasonic released the 1.2 firmware update for this lens. This initial quick test gives me hope that the shake issue may be gone.
Download the firmware from Panasonic here: http://panasonic.jp/support/global/cs/dsc/download/fts/index2.html