At the start of the game, the loot has a load in delay of a couple seconds from render. this was a fix released a while back to make it more fair of OG and S users.
In regards to the mid-game part. First, that sucks, I have it happen, but not all the time. Thats usually just a render delay from all the data being sent to the server and received back by the xbox. I imagine that data (when moving fast and working with other player data) fills up the processor creating a bottleneck when coming in from high speed.