There is a dead dog shown in the climax of Se7en.
Is there any significance to this image?
...but there are a couple of possibilities..both involving Mill's dogs.
The Mills' have dogs in their home...
Firstly, it's possibly as a reference to another draft of the script in which it wasn't Tracy's head in the box but the head of one of Mill's dogs..
...according to Brad Pitt, at one point the studio seriously considered putting the head of Mills’s dog in the box, rather than Mills’s wife.
...“With Se7en, I said, ‘I will do it on one condition – the head stays in the box. Put in the contract that the head stays in the box.’”, the actor told Entertainment Weekly in 2011.
Secondly, possibly as a foreshadowing of what is to come.
Mills refers to his dogs as "the kids"...by showing a dead dog it foreshadows the death of Tracey and her unborn child.
Finally, it's just possibly there for comic effect so that John Doe can say..
"I didn't do that!"
I have an answer but probably you'd call me crazy for it. It think John put that dead dog in there as a benchmark for the Van driver to stop in there. But he did not kill that dog. Because john doesn't strike me as a liar at all and when he says i didn't do that he's right. I guess he found a dead dog and just put it in there. I believe john loves animals just as much as he hates humans.
On the other hand; my answer has a gap in it. John did lie once! The moment he misrepresented himself as a member of the press to get information from the police about Miller's house.