Dullard,
The reason that they have two different measurements on it is due to Federal law. In the computer world (and TVs in the "old" days), the CRT was measureed from the OUTSIDE edge of the CRT diaganally across to the ther OUTSIDE edge. Several years ago, the FCC passed a rule that stated that all TVs sold in the US must have the viewable size listed, not just the outside measurements. The viewable size is the same diaganal measurement, but it only goes to inside corner of the screen where the phosphers (SP) stop. Not the masked region of the screen, not the physical outside dimensions. This is the largest diagonal line the monitor can physically display. Period.
Computer monitors didn't fall under this same umbrella, so they continued to use the outside edge dimension as it is the largest dimension and we all know how marketing people think. Some manufacturers have started to put the viewable dimension on the box as well, but I don't know if that is because they are trying to play nice or if it is a new law I am not familiar with. Either way, the viewable size is the maximum size the monitor can display.
As for the warm up issues, that seems like a very long warm up time to me! Most monitors I have seen have a warm up time measured in seconds before the image stabilizes. Where the image is located on the screen is directly controlled by the yokes magnetic fields. The control circuit should be able to control the voltage to the yoke well enough after only a few seconds to keep your image centered and on target. Heck, it has to hit three seperate guns one on top of the other to get the convergence right (aka: one white point instead of red, green and blue points next to each other). I've never noticed this type of behavior on any of my Sony monitors.