I'm not a proponent for complex Zone of Control (ZOC) mechanics, the simple ZOC that is currently being used for the tactical battles is exactly what I'm suggesting.  On the strategic map, should there be a ZOC for the armies? Civ 5 implements the same simple system for ZOC, keep in mind though that in Civ 5 the tactical battles happen on the strategic map, not a seperate tactical map.

Actions that using the ZOC system on the strategic map will effect:

Harder to sneak past enemy armies.  In my mind this would create more open field battles, rather than sitting in a city and wait to be attacked, or purposely avoiding their army to go straight for a city.  I think this would improve the strategy of army logistics, as you would have to time when to attack, withdraw, gather forces on a strategic level.

Increased emphasis on quick armies.  Armies with increased spead would better be able to avoid ZOC.  I'm not sure whether increasing the emphasis on speedy armies is good, in fact I think that having a speedy army is already on the too much emphasis side of things, however with the ZOC it may reduce their effectiveness as they would need to travel more laterally past armies to avoid losing movement points.

More choke points on the strategic map.  Implementing ZOC would effectively increase the size a choke point needs to be from 1 to 3 squares because armies wouldn't be able to shoot strait past a defending army.  Thereby giving the defending army a chance to attack in the turn the offending army is stuck to 1 move per turn in the ZOC.  I Think this would be an improvement, as it will emphasise other points of land on the strategic map, rather than just the resources.

Caveat, as of .86 BETA I have not noticed any ZOC on the strategic map.  If there is, tell me how it works/doesn't work.