CrossRoads:
I have no way to know what value will give a good result, so lacking anything else, suggested something in the middle of the pot's range.
Well, you are not familiar with LCD displays, you clearly do not hang out on the "Displays" forum. 
The "Vo" terminal is the bias voltage for a chain of five 2k2 resistors (Labelled coincidentally "R1" to "R5") back to the +5V supply (not necessarily Vcc) which determine the multiplexing steps for the LCD panel itself. For most of the common "1602" or "2004" displays, this voltage must be between 3.7 (measured on the display next to me) and 5V, generally about 4.5 to 4.7V. Set to 2.5V the display will simply not work, so "mid-range" turns out to be a particularly unhelpful suggestion. 
Note that I mentioned five 2k2 resistors, to a total of 11k, connected to +5V. A single 470 0hm resistor from Vo to ground will set the contrast voltage to about 4.7V; there is actually little reason to add the other 10k resistor just to make it as if you had connected a potentiometer. If you do add that 10k resistor, you have set the voltage to about 4.5V. A 1k variable resistor from Vo to ground would in fact, provide almost a perfect range of adjustment of the contrast.
Unless the supply voltage varies, the contrast voltage is pretty much a "set and forget" matter, so an externally accessible pot is unnecessary. And conversely (or perversely), if you connect Vo to ground, you can adjust the contrast quite effectively by varying the supply voltage between 4.5 (which happens to be what my USB port is providing to a presently excessive number of breadboarded components) and 5V.
And one other consequence. The 3.3V version of the display has mounted, an ICL7660 or equivalent to provide a full 5V supply not for the driver chips, which operate fine at 3.3V logic, but for the contrast voltage, thus my earlier caveat.