Advantages:
- Easy to set up.
- Cheap to start (somewhat like Heroku). Especially the moment you start optimizing for performance it's easy to cut down on the funds needed each month.
- Scalable. Google takes care of it.
- As someone mentioned versioning. It works as easy as changing the YAML file.
- Deployments are fast and painless.
- Amazing cloud administration with beautiful and easy UI. Unified logs.
- Ease of integration with other Google products and APIs.
Disadvantages:
- Lack of proper support.
- Documentation is sometimes lacking.
- Lock-in. Oh man does it hurt if you want to move away from GAE.
- For python for example, you can only used C based python modules.
- HTTP request 30 seconds. 10mb limit. Datastore is I believe 1mb. Blobstore 50mb.
- Gets expensive the moment apps become bigger (somewhat like Heroku).
I'd definitely wager where your app will be in a month, 3 months, six months and a year and see if GAE is a viable option. Think of API integrations as well.