+1 for jtleathers export mentioned above.
I had the exact same problem: localhost environment with mysql 5.5.38, needed to migrate to a live server with mysql 5.1.73.
My newly-migrated site seems to be working just fine thus far, but as mctenold had asked, I have no idea if I'm losing some kind of important data I may not be aware of.
But what a freaking bugger! I've spent nearly 2 hours on this issue. There are many of us who develop locally using mysql 5.5.X and need to deploy on web hosts using something older.
Currently it seems the only solution is to downgrade my local environment or export with the compatibility settings mentioned above and (maybe?) risk losing some data.
Otto - I realize that your dev sites are used primarily for developing themes/plugins, but a lot of us do actual content population within a localhost environment because it's much faster than doing so on a remote server.