When I'm wielding a reach weapons, like polearms, I have my hands full and generally don't threaten adjecent squares. Does this change if I take Improved Unarmed Strike, for which I don't need arms at all (since I can still kick, ...) or Catch Off-Guard (using the pole as an improvised weapon) feats? Can I for example use the pole of my spear to whack the sorcerer attempting to cast while standing next to me and then stab him when he's leaving the space I threaten with the spear (provided that I have Combat Reflexes)?
I don't threaten with improvised weapons? Where is that said?
I agree with Zmar, nothing in the Improvised Weapons or Attacks of Opportunity does it stop AoOs with improvised weapons (or a nonproficient weapon, which is what an improvised weapon counts as.)