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For a simulation I'm running I have connected an arm to the robot base with a hinge joint. When the robot base rotates around a different axis than the hinge axis, the hinge.angle messes up, and becomes unusable.

Reproduced the angle issue in 2017.2.0f3, and found a relatively simple way to reproduce it in the editor:
1: Create two cubes, cube A and cube B, and give them rigidbodies.
2: The Rigidbody on cube A should be kinematic, such that cube B can hang below cube A.
3: Attach a HingeJoint to cube B and connect it to the Rigidbody on cube A.
4: Attach a simple script to debug the value of hinge.angle. See example script below.
5: Enable limits from -90 to 90 degrees.
6: Enable motor, force 5, targetVelocity 50. (cube B should hit the limit at some point)
7: Play the scenario
8: When cube B hits the limit, use the editor (while still playing the scenario) to switch targetVelocity to -50
9: The hinge.angle will now reset to zero. (Note: The limits still seem to respect the original hinge.angle)

Example debug hinge.angle C#

using UnityEngine;
public class ReportAngle : MonoBehaviour {
private HingeJoint hinge;
void OnGUI () {
if(!hinge) hinge = gameObject.GetComponent(typeof(HingeJoint)) as HingeJoint;
GUI.Label(new Rect(10,10,100,20), "angle: "+hinge.angle);
}
}