There are at least four well-known bugs in Galaga

One bug causes enemies to cease dropping bombs for the rest of the game. To trigger it, destroy all enemies but the two bees in the bottom two rows of the left-most column, then wait, dodging their shots for fifteen minutes or so until they stop dropping any bombs. From that point onward until the end of the game, all enemies will effectively be disarmed (but can still be dangerous kamikazes). This bug was fixed in a later revision of the game. The bug is not present in Namco Museum 50th Anniversary because the later revision of the game was used.
It is possible to control the game during its attract mode. During the game demonstration, at the moment that a boss Galaga begins emitting its tractor beam, the game for some reason pays attention to the joystick and fire button. A player can shoot the boss and continue to play the game for a short while. Sometimes the player's ship will move oddly or be invulnerable until the game demonstration ends; sometimes the game will crash and reset itself harmlessly; rarely a switch error will freeze the game on the error screen.
Unless the machine is set on the hardest difficulty, the game "wraps around" from Stage 255 to Stage 0, causing the game to effectively lock up (although the starfield continues to scroll). This is because the game did not know how to interpret Stage 0.
Player 1's score wraps around at 999,990 (and never registers internally as greater than this number), but Player 2's score has been known to display entire scores over 10,000,000.