At first I was a little annoyed with the control scheme, but as you've made mention later on, it soon becomes part of the challenge, especially when you've got so many cities around in the one area (Try getting to Liege with all the Central Euro cities around it.) Felt the game could've been harder, like with more cities to guess or avoid and with more obstacles, like deserts slowing you down like you've done with the mountains.
A few minor things could be fixed, such as the fact I was awarded Gold despite never making it to Sydney or Beijing until about attempt 40 or so (Think it only recognises how many unique Olympiads I've been to rather than the actual cities, meaning London 1908, 1948 and 2012 are all recognised as a city each rather than just once for London) and the fact I got asked about the Montreal games 4 times in a row.
I could've easily gone on, but decided to declare once I 'broke' the scoreboard, it needs more difficulty in my opinion! (Use cities like New York and Madrid to throw people off, or have strategically placed cities to make it harder to get to cities you want, heck, even add Winter Olympic sites!) I would say reduce the time limit to allow for less mistakes, but getting to Tokyo and Melbourne does take time (I'd say 25 should be the absolute minimum.) The game has its own unique challenge which you were aiming for with the one button spin (Takes a fair while, getting to Rome was a pain, lol), the cities are accurate (only problem is Sidney instead of Sydney) and it was very enjoyable!