Deliberate mistake: Luke's dog in the episode is the same dog used in other episodes involving a dog in the plot.
Other mistake: When Barney is ready to pour the plaster cast into the shoe prints, there are only a few prints on the ground. There should be a continuous set of prints from the barn door to wherever.
Answer: Those "boxes" are valences that used to be very common, before air conditioning. They allow for windows to be open during rain storms. They permit air circulation, without letting the rain in.