Fore and aft changes in center of gravity affect how far the center of mass is from the tail control surfaces and the amount of negative lift the tail has to contribute. I can feel the difference when my (fairly small framed) family moves around in the back cabin.
Aft weight distribution makes the airplane far more sensitive in pitch, reduces drag from the tail negative lift, which slightly increases climb rate and/or forward speed for a given power setting.
I have no idea if "Spirit Airlines weight distribution issue" actually happened, but it's funny so I'll share: https://youtu.be/YvfYK0EEhK4
Magnetic variation in my area is +20° (west) off true north. So if I want to follow longitude line true north I need to fly such that the compass reads 20° NEN. And don't forget to account for the hunks of metal inside the airplane, which can affect the compass differently depending on your heading.