[The Electrician]

I haven't read through it in detail, but the USPS Domestic Mail Manual says in part:

Except under 2.11, the receptacles described in 1.1 may be used only for matter bearing postage. Other than as permitted by 2.10 or 2.11, no part of a mail receptacle may be used to deliver any matter not bearing postage, including items or matter placed upon, supported by, attached to, hung from, or inserted into a mail receptacle. Any mailable matter not bearing postage and found as described above is subject to the same postage as would be paid if it were carried by mail.

And 2.10 and 2.11 talk about newspaper receptacles and delivery.

But I'm not sure whether or how the prescriptions in that manual may take on the power of Federal law, or whether there are other Federal laws that may cover mailbox access and usage. Also, I'm not sure whether dog feces would be classified as "mailable matter", perhaps if classified as ORM-D material, which may be OK to mail.

See http://pe.usps.com/archive/html/dmmarchive0810/D041.htm

[The Electrician]

Then again there is always DMM-601 Mailability, section 12.8: Matter Emitting Obnoxious Odor

Any matter that is a source of an obnoxious odor is nonmailable.

http://pe.usps.gov/text/DMM300/601.htm#1198527