The prohibition of trapping on Shabbat and the parameters regarding domesticated animals, creatures that are not typically trapped, lesson of the Freebird- Tzippor Dror
The parameters of the melacha of tearing for destructive (mekalkel) vs. Constructive (tikkun) purposes, application to breaking a stuck door to let someone out on Shabbat
The deep idea/difference between Emet and Sheker, halacha regarding bringing two letters together on Shabbat- applications to opening and closing books with writing on the side, playing scrabble, puzzles and board games in general
The opinion of Rabbi Yosi that koteiv prohibition also includes symbols or images, applications to fingerprinting, rubik's cube, being filmed by a CCTV, and the Shabbat thermometer