You're right, Gunther and Kim referred to Serrano as well. Shit, maybe they're saving that mystery for the KK movie with Jackie Chan. Also as
@Fedorgasm mentioned above, they never explained who or why Miyagi killed his opponent in the Sekai Taikai. Daniel's mom explains that Miyagi tracked down and beat up the guard who stole his wife's necklace, but that doesn't explain WTF Miyagi was doing at the Sekai Taikai, nor why he killed his opponent. They're probably trying to keep people guessing, and in the movie it'll be revealed that Mr. Han (Jackie Chan) is the great great grandson of the Chinese dude who taught kung fu to Miyagi's great great grandfather. Also Miyagi wanted to fight his ass because David Carradine was stealing everything he worked for, and when he finally killed him at the sekai taikai, Miyagi wasn't surprised MFers.