In Demon's third match he's wearing some sort of army pants. After winning his match he taunts Alex, while he's taunting him you can clearly see him wearing tight black shorts. Then as Demon leaves the canvas, he's wearing the same pants he wore during the match.
The sword that Alex steals at the beginning of the movie is curved with a tassel on the end. The sword that John sells back to him is a straight sword with a tassel on the end.
The sword that Alex steals in the beginning of the movie is called a Japanese Samurai sword. It is in fact a Chines Jian, or double-edged straight sword.