Continuity mistake: When Lynette and Gabrielle are talking to Paul, the boxes Gabrielle are holding change position between shots under her arms. (00:34:30)
Continuity mistake: At one point in episode 1.2 ("Ah, But Underneath"), Susan looks at the note used to blackmail Mary Alice and we can see that it has been folded twice and become somewhat crumpled. Two episodes later in "Who's That Woman?" (1.4) when the girls show the note to Paul, it is almost perfectly smooth with a single horizontal crease.
Answer: He was investigating the lead not the case.