If you include any mini-games, please make them strictly optional. I think at least 90% of the mini-games I have seen are a terrible waste of time (and the developer's resources), and in my opinion, tying mini-games to the player's progress along the main storyline (like it happened in Star Wars: Knights of the Old Republic) is a severe design flaw.
However, I would appreciate a few well-placed puzzles, mysteries and/or riddles. And in a game with turn-based combat, they should not be time-constrained in any way, please. As you might call them mini-games as well, they should only appear in side-quests which you don't have to complete if you want to beat the game.
Solving crime mysteries is something I think would go very well with D:OS, it can offer a lot of interesting dialogue options and it's not that often a part of role-playing games.
