The biggest problem here is your armature is not centered. It is crucial that before beginning any rig always press alt+G/S/R in object mode to clear all transforms on the rig. Crucial
Did I mention it was crucial because it is very crucial 
In short: the center of your armature is not in the center, so the mirror point is not in the center.
Aside from that, you are also witnessing exactly why I never use ‘parent to bone’ for anything in a rig anymore (nope, not even the eyes). The armature is essentially a deformer, and it works best if it is manipulating the mesh through vertex groups. Mirroring and mesh management is far easier that way. Meshes can remain separated within the same object, so there isn’t a reason that I am aware of not to do this. **well perhaps when you have many complex overlapping meshes then it is good to have them separate - like clothing.
In order to mirror this I would suggest first joining the whole mesh into one. Then re-assign each part to the proper bone using vgroups. Just tab into edit mode, hover over a part, press ‘L’ >> ctrl+g to group it, then name the group as the bone name. And apply an armature modifier to the object of course 
Once it is an object you can simply mirror it with the mirror modifier and all the vertex groups will be intact. You will have to manually create empty groups with the opposite side name for the mirror to deform asymmetrically.
However, I’m actually having trouble with your rig…
I’m afraid I must not have looked closely enough at it when you first asked me (sorry about that :o). I didn’t realize you were using the action constraint to correct the tilt! I had assumed it was entirely constraint based. The action constraint will not mirror (although the animation can be manually transferred over using the mirror-pose function, quite easily). But I wouldn’t suggest using the action constraint as a way to correct a mechanical rig.
I have taken the time to create a working version as I have mentioned. Found a new solution for the rig, although a bit of a hack because I used the stretch-to constraint for the upper arm, heh heh. There is a simple trick for re-centering an armature which I will cover in my video… thanks for reminding me of several issues I need to cover in my tutorials
In fact, would you mind if I used this in the video and showed how to fix it? It perfectly sums up why it is so important to clear transforms before beginning 
@MarkJoel60
Bones can be extracted from an armature with ctrl+alt+p and then joined into the other armature in object mode with ctrl+j. It’s not perfect, but it often works 
Attachments
AirCar6_tinker.blend (477 KB)