The washout of the fourth tee was clearly due poor construction of an embankment. The culvert looks awfully small and there's no diaphragms or collars to prevent seepage along the outside edge of the pipe. The trench for the culvert was likely poorly compacted when it was backfilled.
The washout along the cart path (hole?), it appears that there wasn't any provision for drainage off of the cart path except down a steep slope. In addition, the minor mounding along the path (to hide it from view) likely caused the water to build up there. In that case, a small rivulet becomes a washout quite quickly.
Neither appears to have anything to do with shifting dunes.