Plot hole: When Zach Young's grandfather died, Zach was said to be the sole heir of the fortune. However, Noah Taylor (the grandfather) had a daughter that appeared several times while Mike Delfino was looking for Deirdre. Where was Kendra Taylor while Zachary Young was spending Noah's fortune on dresses for Gabrielle Solis? Why didn't she claim her share? She simply disappeared.
Plot hole: It says on Mary-Alice's tomb stone that she died on September 26th 2004, which was a Sunday, yet in the first episode, she says that she died on a Thursday.
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.
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.
Answer: He was investigating the lead not the case.