Plot hole: Several days must have passed between the teaser of this episode and the rest of it, since Gabrielle has had time to make up (very professional-looking) cards and posters, gotten several dozen volunteers and reserved dresses for many of them, yet Paul has only just gotten around to disposing of Mrs. Huber's body and trying to wash the blood out of his shirt. Even if we assume the teaser takes place right after the end of the last episode (when Paul murdered her), that's still several days of keeping a rotting corpse and enough evidence to put him away for life around his house.
Plot hole: Rex is in the hospital for having a minor heart attack and is awaiting surgery to receive a pacemaker. 1) He isn't connected to an ECG or any other heart monitor so no one is aware of his heart attack. 2) They ran blood tests and checked his potassium levels. They would have also checked the concentration of his medication in his blood. (This should have been done earlier in the season too when they first discovered his medications were not working.) Zero concentration of medication in his blood could throw suspicions on his wife just as easily intentionally giving him potassium.
Answer: He was investigating the lead not the case.