The container supposedly used for the frozen sperm could never hold liquid nitrogen. Liquid nitrogen should not be transported in closed containers, unless they are equipped in a pressure relief valve (which this coffee thermos clearly didn't have). Also, the characters are quite careless in handling this dangerous substance.
Police do not put crime scene tape on the stairs of a missing girl's house. No proof a crime has been committed.
In the recap, the police officer calls in code 10-36 and says it means missing child. But in reality, in both police code and CB radio code 10-36 means TIMECHECK.
It makes no sense for the Abbotts to call the police before calling people Amy could be with, such as her grandmother (who she ended up being with.)