I like PeQuersi! I have never played Reversi before, but first time I opened your program, I won! Though several times later I lost (but then, I can console yourself that computer sometimes grabs my pebbles ;-).

1. Sometimes, after one game is finished, I click "New Game", it creates new field, but the count outside the field doesn't change, and I cannot make a single move, I have to restart the program.

2. Several times, when I won the game, the program didn't show the message that I won the game. No possible moves, and no message about the end of the game.

Current design is all correct.

What about a feature of playing against another player (or against yourself instead of computer? What about computer having first move?

Does the computer play randomly - or it chooses the best possible move? In other words, is it a formidable artificial intelligence opponent or a guesser? Or something in between?

Some warnings when I run it from terminal:
WARNING:root:Maemo detected
WARNING:root:OpenGL acceleration not available
'Main' object has no attribute 'view'

And you could add portrait mode support.