I foound it really difficult to tell which episodes were in what order. I didn't notice an episode number when they aired. On the tv guide channel, sometimes they'd mark an episode as new and when I sat down to watch it, I had seen it before a few nights ago! Last night I checked to see what was on and it said American Ninja Warrior was at the Vegas Finals. However, that's what it's been the last few episode. I wish they had made it clearer this was the final episode.
However, I still wouldn't have been able to watch it and Dancing With the Stars. Even if I had known it was the final episode, I probably would have had to hold off watching it anyway.
Plus, I had tried looking at the official site over the weekend to verify when the finale would be. All the official site had was that the show is on Tuesday nights. It made no mention (at least that I saw) of the finale being on a different night.