This refers to a weekend (or evening perhaps) that is so low key and lacking in events that on a volume scale it is undectable to humans...just like a dog's whistle.
Matt: How was your weekend man?
Jay: Effing horrible. Friday night my ride bailed and Saturday/Sunday I stayed in studying...my weekend was so low key only the dogs were aware.
Matt: Ahh you had a dog whistle weekend...lame.