Frasier says that his son Frederick is 13. Frederick's birth in _Cheers_ took place late in 1989, so Frederick should be 11.
When Frederick returns to the cabin, asking permission to eat sloppy joes with Melody, Melody's scarf changes positions throughout the scene.
When Frederick asks about a bathroom, Martin says that all of outdoors is the bathroom, implying that there is no bathroom. In reality, the rental cabin owner would be obligated to provide adequate toilet facilities, whether in the form of an outhouse or an indoor toilet.