Defeating Allen in Mission 3 without taking any damage or by killing him with just grenades, a tiny hidden UFO can be seen towards the top of the screen.
Nazca, the company who created the first Metal Slug, didn't have an official logo, and since they were bought by SNK after the first game, their name was never displayed. However, the tiles of the first game contain two logos for the company, one static and one spinning. Neither of them were used in the actual game, though there is still an unused jingle to play alongside them in the game's code.
There are several animations of the players shooting and throwing things in several directions while facing the alternate direction. It appears that players may have been able to shoot and throw grenades behind them without turning around. Some of the animations can actually be seen in the game. This can be done by releasing your parachute and shooting left.