I don't know of any hay that doesn't contain a few leaves and sticks. Hay fields are hardly pristine, grass only places. Other things grow in there too, and the farmer generally bales all of it up together.
That hay in those pictures looks pretty decent.
Oh I expect leaves and sticks and such but I couldn't remember if it was oak leaves that are bad for horses? Must not be. The stick I took out the other day was half the length of the bale and about 2in wide. That seems a little big to me but maybe not then.
That hay would be ok if it wasn't full of mold and a pile of dirt/dust comes out after you drop it from the loft. Like I said that is the best looking stuff. Most of it is very stemy.
My horse lost a lot of weight going into winter because she wouldn't eat the crap hay that she was getting then. I had to buy my own bales of alfalfa hay to put in her stall plus I went thru about another 5 bags of alfalfa pellets a month.
Oh and I should mention my horse does not get pasture, hay only.