We all know those SPECIAL points are very precious. I've been wondering what the minimum level of Perception is to still reveal red ticks (for enemies) on the Direction compass in the lower left corner. Anyone know?

I believe that the higher your Perception, the larger your "circle of awareness" is. I could be wrong...

Yes, Perception dictates how far away you detect enemies (or friends, for that matter... just green as non-hostile units rather than red as hostile units).

However, a lot also depends on your environment, at least from a practical viewpoint. If I have a clear line of sight, I can see enemies (and shoot them) regardless of whether or not they are red on my compass (and assuming I have a long range weapon with or without scoping).

some perks require a perception of 6. if you don't want those perks, 4 might work for you. keep in mine perception also effect some skills.