Other mistake: After scuba divers got Tess' body out of the water, Peter asked Det. Martinez who she was. Martinez replied, "She and Charles were common law husband and wife." Peter later asked if he would be notifying Tess' family. Martinez replied, "We don't even know Tess was her real name." It doesn't make sense that Martinez could know Charles and Tess were common law spouses if he wasn't sure who Tess really was. Also, N. Carolina never recognized common law marriage and Florida abolished it in 1968.
Other mistake: Det. Martinez told Peter he couldn't do anything about his belief that Charles was in his penthouse (and took his dog) without the necessary evidence. However, the detective filed stalking charges against Peter based on Charles' statement that he was being stalked, which was without evidence. The charge of stalking was also far-fetched and the detective should have had enough sense to realise that Charles would not be in fear of his safety over Peter's presence or behavior.
Plot hole: Charles was a con man, going up the east coast (Florida and North Carolina) offering to do cheap storm repairs, taking the 50% cash down-payment and moving on (fleeing to the next location). As such, he would try to stay away from police/law enforcement officers and not call attention to himself. Filing (bogus) criminal complaints against Peter put Charles in direct contact with the police - a very risky and stupid move on his part.