I had a heck of a time getting it to work with Zen Cart, because my client had some goofy shipping issues. Once we *did* get it working, the biggest problem I had was that no matter what we did, Google Checkout would not let us set the priority/sort order of the shipping choices (which were from a UPS feed), so that the fastest and most expensive was always on top (and checked by default) Changing the sort order in Zen Cart didn't help. Rather than risk a bunch of angry customers who likely would get caught by this, we took Google Checkout off entirely for the time being until we can get some kind of a fix or workaround.
Poor integration. Users are often confused how to interact with the originating ecommerce site since they never login to that site in most cases and emails are communicated anonymously for many customers.
100% email driven communications. If someone initiates a chargeback and you miss the email that says you have 24 hours to respond you're SOL. They send out so many automated messages for whatever reason its hard to discern what is legit/true and not just a glitch of their systems.
And like others have said, the shipping integration is absolutely horrendous. Having the timeout default to checkout conditions in 75% of the orders stinks
Some people love the google checkout buttons and swear by it but i think many people are confused. I find it slightly more work handling google checkout but worth it since they guarantee the transaction up to a certain dollar amount. Thats the only reason i stick to it. I don't think it makes much difference in my adwords ROI though.. nice little trade off in fees but not enough people use GC to make a dent in my processing costs.