One school of thought says, "Make each characters marks upon it colored so we can see who does what."
The other school states, "Lock it so only the leader can draw on it."
Let's explore the good and bad sides of each idea please?
Assign each character a color representing their drawing or pinging on the map.

Groups can now see who is the annoying dipstick that scribbles or excessively pings the maps in game.

There is no ability to "kick" annoying jerkwads from a group once in a mission, so other than "knowing" specifically who the jerkwad is, it doesn't prevent this from occurring whatsoever.
Solution:
Add an "in-game" kick function for the party leader - to drop idiots on the fly.
Assign the leader only the right to draw notations on the radar/compass.

Don't have to worry about colors, jerkwads, or what have you. 1 person, 1 notation, period.

The leader of a group isn't always the one who "leads" the mission.
Solution:
Allow the party leader to designate one person as "cartographer" who has sole ability to notate the radar/compass.
More input please?
Talesin