On Asteroids games, the only place where the game serial number appeared was on the foil sticker located on the rear of the cabinet, bottom edge of the upper slanted panel. Actually, there were two stickers side by side. The paper sticker gave the electrical info on the game. The foil sticker had the model and serial numbers. Sometimes the black printing on the foil sticker disappears with age, but the model and serial numbers were actually stamped into the foil and remain readable. I've attached a pic.
There will be hand written numbers on the A/R board, game board, and on the inside of the cabinet. These are serial numbers of individual components, not the overall serial number of the game. It wasn't until later (Battlezone production) that Atari started slapping the little game serial number stickers on all the components inside the cabinet.
Early production Asteroids games had:
"owl eye" coin door.
G05-801 monitor.
plexi bezel with the text printed in yellow (later switched to white).
sides of cabinet are plywood (later switched to particle board).
early revs of the game pcb (-02, for example).
burn at the bottom of the screen is "Asteroids by Atari" which is code rev 1. (code rev 2 had "© 1979 Atari" at the bottom).
small copyright sticker on the bottom of the screen.
plywood on underside of control panel for mounting of buttons and leaf switches.
I happen to own Asteroids S/N 434 - which qualifies as very early production. I have a few photos of it at
https://picasaweb.google.com/108339843851140624101/AsteroidsSN434#