I did recall one incident where the plane got out of balance because of passengers moving in concert.

https://www.indiatoday.in/india/story/asaram-bapu-rape-accus...

Abso-freaking-lutly. The permitted range for the CG (longitudinally) — denoted as "% of MAC", for Mean Aerodynamic Chord — is quite narrow, and you prefer to stay away from the "edges" of that range whenever possible.

The distribution of pax and baggage are chosen so as ensure its within the range. IOW, they don't book Row 1 then 2 then 3, etc, — sold seats are sprinkled across the aircraft as it's filled.

I've been told when the flight attendants are moving forward and back with the beverage service you can watch the trim wheel turn as the autopilot maintains correct AOA.

When flying a small airplane in Asia we were all weighted individually, and distributed around the plane accordingly.

There was a plane crash in the Congo that was reportedly due to everyone running away from a crocodile. https://en.wikipedia.org/wiki/2010_Bandundu_Filair_Let_L-410...

On the ATR-72 [0] there is an extra leg that folds down at the back of the plane to stop it tipping over, and passengers at the front half must remain seated until the rear pax have left, so there must be some danger of unbalancing. These are weird planes in that the cargo is stored at the front, behind the pilots, and the only door is at the rear. They are prop planes, the 72 being a stretched 42, I believe.

0. https://en.wikipedia.org/wiki/ATR_72