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Cohesion wise, militia are not being properly penalized for being out of state. In fact, militia outside of their home state have 5 more max cohesion than those who are at home. Discipline and movement penalties for being out of state are working correctly, it is only the cohesion.

The source of this bug is located in the GameLogic.opt file. Under the Home Area Penalty/Bonus there is this entry:

areaOutsideHomeTQ = -3 // TQ (and 5 time that to max cohesion)

This value is producing a positive instead of a negative (only for cohesion, not TQ). I verified this by changing the -3 value to -15, the result was an overall increase to militia of 60 maximum cohesion points. When I changed the value to a +3, it gave the proper result of in-state militia having 10 more max cohesion than out of state militia. However, the discipline value was not decreased for being out of state.

Good catch! I hope they do another patch.

Would upgrading a running game be without danger?

And I see more values in the file:
areaOutsideHomeAbi = -1 // -1 level to abies (can render them inactive)
areaOutsideHomeStr = -2 // Strategic
areaOutsideHomeOff = -2 // Offensive
areaOutsideHomeDef = -1 // Defensive
areaOutsideHomeTQ = -3 // TQ (and 5 time that to max cohesion)
areaOutsideHomeMR = 66 // Move Ratio Coeff (x0.66) // [changed 120921 from 0.33]
cohLocalAreaBonus = 10 // bonus to max cohesion if at home

Do all the others work correctly?

You should be able to change it mid-game, though it will affect all your games.

I'm not sure if the other values work right, I think they do, I haven't noticed them not working. The out of state movement penalty does work. I think those values for strategic, offensive, and defensive are for corps outside their army commanders range. Interesting bit about how its lowers ability levels by one... I wonder if corps commanders can actually have their traits turned off if they get out of range.