Jon and George,

Actually, I think the Mesa sign code
likely would be found constitutional (from what I know of the
ordinance, which is little).  BTW: To be clear, I think the policy
is ridiculous.  However, it probably would be viewed as a
content-neutral regulation, as opposed to prohibiting specific content,
such as an unappealing piece of art.  In other words, it doesn’t
regulate what is said in the sign, but regulates the % of a window
covered by signs.   Another key aspect of the First Amendment
analysis in these types of cases is whether the ordinance completely
prohibits a key means of communication (it doesn’t here–signs still
are allowed).

Once (and if) the First Amendment argument is out of the way,
the issue turns to whether the zoning advances a legitimate
governmental interest.  Local governments are given a lot of
deference in zoning, and aesthetics is usually recognized as being a
legitimate interest (see the cases below).

This is a really complicated legal issue and the case will turn on very specific facts.  Here is an article from the First Amendment Center on ordinances prohibiting political signs and another article on sign ordinances and the First Amendment (in general).

Two leading U.S. Supreme Court cases: City of Ladue v. Gilleo and Metromedia v. San Diego.