Generally I feel this is a flaw in Arkham in that it is usually better to simply not do anything than take encounters; at best many are a waste of time and at worst they can be the reason you lost the game, and yet I feel they are supposed to be the core of the Arkham experience. If I were to change things about the game it would be:
1. Make encounters at stable locations more beneficial. Encounters where something bad just happens to you, no roll and no chance at one. Frequently, it doesn't even make sense: I get a roll if I find out I've been washing my face in human blood, but a spooky ink stain is just too much for me to even hope to resist? Poppycock. If a location has a secondary benefit, then it can retain a few purely negative encounters, but even these should have rolls. Stable locations with no secondary function should be purely beneficial, have very small chance of a negative encounter, or not exist.
2. Make an encounter mandatory at a location even if you use it's special ability, and then move using location special abilities to the end of the movement phase, which is what happens in 90% of my games anyway.
3. Have street encounters, which should be mostly bad: You get mugged, you get run over, you get arrested for loitering, a monster ambushes you, a flyer ambushes you, a monster creeps closer toward you, whatever. It makes monster hunting more dangerous and removes the urge to just chill in the street instead of having encounters. If you get moved to the street by a location, guess what? Street encounter!
4. Unstable locations require you to pass a successful encounter to receive a clue, instead of it being a sure thing. Unstable locations should be 90% bad results, with a few high risk/high reward scenarios.
5. Other World encounters should be where the gloves come off. If I have a better chance of walking out of the Abyss with my Sanity intact than South Church, I think we messed something up.
That's just a personal opinion though, and I'm not sure I'd want to deal with rebuilding the game from the ground up.