Also I find Beast doesn't auto-chase, alot of the time.  Can be almost as frustrating as getting kited to death if you have your enemy down to 100 hp and he gets away by *drifiting slowly* out of present attack radius

This was really one of the major features I wish they would have fixed for 1A.  This is why stuns are so important.  Without them melee heroes, no matter how fast, cannot kill you with their physical attacks(assumming you actually start moving before you die).  DotA has this problem to an extent as well but not nearly to the extent of Demigod.  I think the solution is to not require a unit to stop moving in order to attack.  It'd work similiar to the ways tanks shoot in SUPCOM where you could constantly circle your opponent with move commands and you will hit him as long as you are in range.

Also, I think ranged units should have to stop to fire.

I like the idea of allowing melee heroes to attack out of a run.  Slowing them down during the attack, or forcing them to stop for a half-second after the attack would allow running to still be effective.  It was not as noticeable in Beta 1 because the only melee Demigod was rather slow (Rook).  UB is much faster, however.  In fact, several of his abilities involve speeding him up or slowing the enemy down.  These features are rather useless right now, because regardless of how much faster the UB is, he cannot attack a fleeing foe.  Personally, I think an animation for attacking out of a run with a brief pause afterward would be the best.