During flight specifically during proving grounds missions, I noticed my target reticle won't stay still, it likes to jggle around a little bit and it gets annoying and hard for me to shoot still standing targets. I think this issue also remains in TIE Fighter as well because I remember seeing it happen there too during the training missions. Does anybody else have this problem?

There's two causes:

1. Open dosbox_xwing.conf, find timed=true and set it to timed=false.

2. There is a bug in the engine where if your ship is facing straight up or straight down, your view is "repelled" away from those directions. Unfortunately there's no fix for this, and it's there even in X-Wing Alliance. Fortunately, you're unlikely to run into this outside of the training mission since it would be pure chance.

Gimbal lock, is called.
It is also there when dogfighting if you, for example, try ambush TIEs as they come out from a Star Destroyer's hangar by placing yourself directly below.

Easy to solve if replacing roll/pitch/yaw with quaternions in the code, but we don't have access to the source code. Something to keep in mind if someone ever thinks on making a remake, though. :)