The vapor barrier on the insulation was installed backwards. The vapor barrier must face the warm side of the building to prevent moisture migration into the insulation and framing system.
Inadequate ventilation was also noted - you can see particles floating in view of the camera. Cellulose insulation visible in the attic area at the time of the inspection. It should be noted that this insulation material could be extremely flammable if it has not been treated with fire resistant chemicals
Cave and camel crickets are of little economic importance except as a nuisance in buildings and homes, especially basements. They are usually "accidental invaders" that wander in from adjacent areas. They may reproduce indoors, especially in situations that provide continuous dark, moist conditions, such as a basement, shower or laundry area, as well as organic debris (e.g. compost heaps) to serve as food.
Locating and identifying rot and wood destroying insect damage as well as how the extensive the damage is part of what a home inspector and termite inspector is required to do by licensing laws.