None

It's just that the real Detective Toschi actually liked them so David Fincher added to the realism of the film by having Ruffalo eat them too.

Director Fincher tries to recreate many of the actual details of his real-life characters. He has Ruffalo appear in a bowtie, which Toschi wore. Fincher often gets the real details, but ironically they sometimes lack meaning. He has Ruffalo eat animal crackers; Toschi had a penchant for them. But it winds up being a detail that seems more contrived than real.

^Source

Ruffalo confirms..via Collider

Mark [Ruffalo] I feel like it was a fair portrayal of Dave Toschi in the little time I had to do it in.

[Collider] Including the animal crackers.?

Mark: That’s Dave Toschi. It’s classic Toschi, the Tiparillos, the animal crackers and I hope the way he talks.

[C]The bow tie too?

Mark: Dave Toschi. Call me Dave Toschi.