Luggage shifting generally isn't a problem, since large luggage volumes are containerized and therefore compartmentalized, and in smaller jets like corporate aircraft, the luggage is confined to a small space.
With swept wing airplanes, fuel burn causes a natural and significant C of G shift as fuel C of G moves forward as fuel level declines in the outer extremities of the tanks, which is more aft.
If the plane has a center wing tank that is depleted first, the C of G shifts aft, then forward during the flight. When you do weight and balance on a jet with a center tank, the fuel C of G curve on the weight and balance graph looks like a bit like a cursive letter Z in depicting this shift, and the curve has to respect the C of G limits at all points.
People moving around will have subtle effects on trim, but nothing like the fuel effects in a swept wing airplane, unless you have entire groups all moving at once. It's all about proportion. If you are a small two seat homebuilt, just leaning forward in your seat will give you a 5 or 10 knot increase in trim speed.
In any case, any C of G shift changes the airplane's trim nose up (slower) or nose down (faster). If you are hand flying, you will have to adjust trim as you notice the plane pitching in response to the change in trim. Most of the time however, the autopilot is on, and it takes care of the trim on its own.
If you are hand flying and some passengers move forward or aft enough to make a noticeable change, you will just be instinctively blipping the trim to make the airplane do what you want.