Stealth section could be fun; in my particularly case I wasn't actually thinking of having to properly sneak up on a character, I was just thinking you'd simply approach from the correct direction so the character is facing the other way, i.e - if she's facing north, then you need to find a way to approach from the south. However, adding a stealth mini-game for that correct approach could be excellent fun!
V-mode shows how this might be possible as well; for example, instead of a sex-scene you're spying on you'd be moving slowly forward, and if the character seems about to detect you, you can hit the hide button to duck into the nearest cover. This can be made more challenging if hiding only works while you're near suitable cover, so you have to try and decide whether you can make it to the next piece or if you should wait.
As I mentioned in another thread, I'd love to see some of the current and past puzzles re-appear in a simplified form for those that missed them. The best example being the hunt for Anne's glasses; instead of having all her scenes available all the time, you'd be given the task of finding her glasses, but instead of the current, relatively tricky hunt (unless you know the quick route to finish) it'd be something simpler, like going to where she last saw them and talking to characters there, to find out who has hidden them, then ask that character to find out where they hid the glasses; dead straightforward but it adds a minor challenge, which can make the reward seem all the sweeter. Probably best added once persistent game-state is added so you don't have to find the glasses every time, plus persistent state can be used to make sure you actually do the search properly, i.e - the glasses wouldn't appear until you've confronted the thief, but they'll just deny stealing them unless you've spoken to other characters that saw them do it, and those characters won't know anything about it unless you speak to Anne first.
A chase mini-game could be fun, with a fast character that runs away and you've got to try and find clues as to where they went, such as dropped items, confused characters they ran past, and so-on.
In fact, I'm a fan of detective work in general, so an area could contain clues, and when you think you've found what you need you speak to the character there and they'll ask questions that you should be able to answer if you found everything. This could be another good idea for a challenging type girl; basically you're trying to convince her that you know her, so to do this you explore her room for clues, and when she asks you questions you can answer them, and if you do well enough (you know things that she wouldn't just tell anybody) she's really apologetic at having forgotten you, and eager to make up for it…