I've played one game so far (by myself playing all four sides) and the most confusing part of the rules for this game are the movement rules. Below is what I think are the correct rules. Hopefully this summary is correct.
There are essentially two movement phases in each turn. The initial Maneuvers movement and the final Invasion movement. "Maneuvers" and "Invasion" are not necessarily descriptive of what happens during these phases, so I will add "Initial" and "Final" to clarify what is going on.
In the initial maneuvers movement phase, all units can move except for infantry and partisans. Mechanical Units move 1, helicopters move 2, and bombers move 4. Infantry and partisans can move if they're carried by a mobile unit. At the end of the initial maneuvers movement phase, all units must be in a friendly territory with the following two exceptions
1. Bombers can end in an enemy territory with a battle marker on it.
2. Helicopters can end in an unoccupied non-city territory. This is called "scouting", and the helicopter is not allowed to move or attack for the rest of the turn.
In the final invasion movement phase, all units can move the same number of territories as above, but the infantry and partisans can move 1 all on their own. At the end of the final invasion movement phase, all units must be in a friendly territory, or an empty enemy territory with a battle marker.
So, that means that over the course of your turn, a bomber can move 8 spaces, 4 in the initial maneuvers phase and 4 in the final invasion phase.