Thanks for this info, Huracan. So, looks like it is not only important to sit in the specified seat/row but to also leave it in the right order.
Yes, don't worry much about it, they collect the Green Card at the moment you enter your row to seat. Only problem could be if you switch seats with your spouse or someone else once you enter the row of seats. When entering the row you do it from the center aisle of the theater, when you leave you leave on the lateral aisle. Yes, it is important not to try to pass people when leaving your row, just leave in order I don't remember exactly, but I think they explain the procedure right at the end of the ceremony. I would assume that if they have some issues is because the Green Cards for a row got mixed up or they have missing certificates or something like that. The procedure itself is quite simple, and it worked great in my row.