When setting the heading control directly north (0 degrees or 360 degrees) the rover tends to swerve randomly and immediately correcting.

This looks to be due to a simple rounding error with a potentially simple fix. The code currently shows:

    public static double ClampDegrees180(double angle)
    {
        angle = ClampDegrees360(angle);
        if (angle > 180) angle -= 360;
        return angle;
    }

The following change may fix this bug

    public static double ClampDegrees180(double angle)
    {
        angle = angle % 180.0;
        if (angle < 0) return angle + 180.0;
        else return angle;
    }

Great program and very clean code.

OK, I reproduced the issue, but I don't think it's due to rounding errors. Rather, the problem is that the autopilot is using a moving average of the vessel heading to determine how to steer. But this moving average is not well behaved when the heading crosses from 360 degrees to 0 degrees, or vice versa, which causes the glitches. I'll try changing it to use the instantaneous heading, which should be free of this problem.

The above change should fix it; if you want to try out a dev build with the fix, replace your MechJeb2.dll with the one available here: http://jenkins.mumech.com/job/MechJeb2/

Confirming it is fixed on my end as well.