Other mistake: When Somerset goes back to the man's house alone, he cuts a sticker on the door with his switch-blade to get in. The first error is the sticker is on the inside and it says "Keep Out." The best part about it is the door opens inward. How did they put the sticker on the inside and then exit? (00:20:45)
Continuity mistake: When Somerset is in the taxi on his way to the Library, he is wearing a blue and white shirt, yet when he arrives at the Library, his shirt is completely white. (00:24:42)
Continuity mistake: The amount of the name that is left on the door when the janitor is scraping it off changes - it goes from being Some.... to Somerset. (00:18:35)
Continuity mistake: The phone on Brad Pitt's desk changes position (parallel to the desk, then angled towards Brad Pitt, then angled away from him) several times when he first goes into his new office. (00:29:50)
Continuity mistake: At the Greed crime scene, when Brad Pitt first gets up from the table with the remote control, his tie is tucked into his shirt. When he walks towards the TV, the amount of tie sticking out of the shirt increases. (00:17:10)
Continuity mistake: At the beginning, when Brad Pitt gets out of bed there is a quilted cover on the mattress. Then when he goes to answer the phone it has a plain sheet. (00:06:20)
Continuity mistake: In the final scene where they are in the desert, the sun hits John Doe first on the left and then on the right side of his face in two different takes.
Continuity mistake: When Brad Pitt gets up from bed, Gwyneth has a light colored blanket over her. When Pitt is dressing in front of the mirror, the reflection shows that Gwyneth now has a dark colored cloth over her body. This dark cloth disappears when Pitt picks up the phone.
Continuity mistake: At the precinct when Somerset recites the seven deadly sins for both Mills and the police captain to hear, Somerset has two crime scene photos in his hands. He holds the gluttony photo with three fingers, then only two, once the angle changes. (00:23:45)
Continuity mistake: When the three protagonists are in the desert towards the end of the movie, as Mills angrily points the gun at John Doe's head, saying to him "You liar, you f***ing liar", some clouds can be seen behind him, but when the angle changes the clouds have vanished.
Answer: I've seen se7en hundreds of times, and I've always wondered what Mills was trying to say to Somerset, and here's my take. If you've noticed, the recurring theme between the two was their conflicting views on how they see the world around them. Somerset is the grizzled, experienced detective who has been through the ringer, so he's views are more pessimistic in nature. Which I can sympathize with. Mills being the rookie detective that he is, was the optimistic, "I'll be the hero" kind of guy. So much so that Somerset called him out for being too Naive, and that he can't be like that. So getting back to the question at hand. During the chest shaving scene, I believe Mills was about to tell Somerset that his dark pessimistic view of the world around them makes sense. Mills wanted to say that Somerset was right, which he wasn't able to bring himself to do.