Stupidity: When Amy tries to use the security cameras at Desi's house to make it look like he raped her, wouldn't the cops be curious as to why there was just one little scene - and not 30 days worth of footage? Wouldn't they question what happened to the rest of the footage (showing her being looked after by Desi and living comfortably), and why that little bit showing her crawling on the ground was left undeleted. Also she tied lace around her hands. Anyone could break material like that if they tried hard enough. Why would Desi risk that?
Stupidity: In the exciting denouement when the SS company approach the ostensibly disabled Sherman, the SS would have just walked around it. A burning tank was a common occurrence. I doubt they would start climbing on it and they certainly wouldn't start charging at it individually as to get mowed down. The SS were well trained units. Such stupidity is unlikely.
Stupidity: Liv was a graduate psychology student when she met Bill and, after marriage and being physically abused, knew that the leaving Bill put her in a (potentially) very dangerous situation. It is best if the abuser does not know where the victim is "hiding" after separation, but Liv brought along Carol to pick up the kids - and they were going to be staying at Carol's house.
Suggested correction: She brought Carol along as a chaperone/protection when she picked up her kids. She didn't announce to Bill that that would be where she was going to be staying, she only told her kids that when they had already driven away from the house. Bill didn't seem to know who Carol was anyway. Even if he did manage to find out where she went, she could have easily got a restraining order against him.
It is more likely that she brought Carol along for emotional support and to act as a witness. If she were looking for protection, she would have used a police escort. It was implied they were going to be staying at Carol's, but, even if not, Carol's presence offered Bill a hint of where to start looking for Liv, and there should not be any leads. Liv unwittingly put Carol in a potentially dangerous situation - if Bill went to Carol's looking for Liv, and Carol truly did not know where she went, Bill would insist that she did and threaten or do worse if Carol didn't tell him. Remember how Bill drilled all the kids about where Liv went, checked their phones, accused Sam of knowing more, then got them into the car and drove like a maniac? Bill has a temper and propensity toward violence (at least when drinking, which he did everyday). Court orders take time to get, but are not very effective. Numerous women who had restraining orders against abusers ended up six feet under.