Twice now after completing the Civil War Hadvar is waiting inside Whiterun. As soon as I go in, whether through the entrance of via fast travel, he's there. Pulls out his sword as if we are in combat and follows me around. He goes into Dragonreach with me, but wont follow me anywhere else inside. He even follows me outside the city, but parts ways with me as soon as we're outside. He reappears once back in Whiterun.

I think He's just stuck in memory or something. He goes away the next time I play Skyrim.