Database with all LSS Chess 960 tournaments finished up to and including December 2012. 7308 games in zipped PGN format.
After downloading the file and adding it to my database, I developed some queries to identify short games. Of the 7308 games, I found over 1000 that finished in ten moves or less. Many of these were games that had been abandoned by one of the players after only a few moves, but some were genuinely short games. One way to identify real games was where they contained the checkmate ('#') symbol. Consider the following start position (SP).
One game with this SP lasted only three moves -- 1.Nf3 Nf6 2.Ne5 Ne4 3.Nxf7# 1-0 -- ending in a smothered mate. Many of the short checkmates were more examples of smothered mate, although I also found quite a few that were the result of a Queen and Bishop battery on a long diagonal checkmating the enemy King sitting on b8 or g8.
In the past, I've seen these short games used as 'proof' that chess960 is somehow deficient because it permits them. The same argument would say that traditional chess is deficient because it permits Fool's mate (1.f3 e5 2.g4 Qh4#).
Short mates are more a reflection of a player's skill than of a game's shortcomings. It is absolutely essential to look at threats created by the opponent's last move. In chess960, this often means threats created on the first move.