For the winning intinerary, it's a moot point as both Europe and Asia are represented at different stops.
Istanbul Atatürk (TAV) airport is Europe, Sabiha Gökçen (SAW) is in Asia. The border is the straight of Bosporus.
Continents are a rather vague concept[1]. Any definition is going to be arbitrary. For the purposes of your contest, I think the spirit would be to have gone to the continents "proper", i.e. I wouldn't count Guam at all, but say the continents are the mainlands of: NA, SA, Africa, Europe, Asia, Australia, Antarctica. I'd be inclined to allow New Zealand as part of Australia as the only exception.
1: http://www.youtube.com/watch?v=3uBcq1x7P34