1) The data is not persistent -- meaning, if your server dies, you loose your database with it. Rebooting the server gives you a clean slate.

This theoretically can be addressed with a complex backup/redundancy model, but frankly, it's not worth the trouble. Alternatively, you can use a distributed filesystem based on S3, but the performance will be poor. Long story short, your database is your bread and butter, and EC2 simply can't provide the basic services required to run a DB efficiently.

2) Dynamic DNS. Extra headaches, simply not worth it.

EC2 was not designed for persistent data storage, it's a compute cloud.