I don't know if the procedure is different for diesels, but I think oil should be checked hot, usually a few minutes after shutting down the engine. Also, it seems like both sides of the dipstick ought to be interchangeable; you can stick it in one way, stick it in the other way, and it shouldn't matter. Is the reading consistent, independent of orientation (e.g. the higher reading always on the front of the dipstick?)
Anyways, I'd go with the higher mark, dump in a quart of oil, and figure that even if the lower mark was accurate, I'd still be within the min and max levels.
p.s. I run into this problem *all the time* trying to check my ATF level.