Pros:
built-in ui for unified logs
built-in web interface for task queues
built-in indexes on list of primary objects.
Cons:
loose logs very fast
VERY expensive
VERY expensive
VERY expensive
Un-hackable. Scales because you're obligated to code in a way that scales.
Longer development cycles. Sometimes you just want to hack something together and throw it away after 5 hors. With appengine you have to proper code it and write a lot of stuff to make it sure it scales. You can't just do a "find . | grep .avi | xargs ffmpeg -compress ...." :)
You will loose hours trying to do the simplest tasks like sending push notifications to APNS (iPhone). Although it's fine if you only want to support android in the future.
Terrible to make cleanups on the database. It's a HUGE pain in the ass to fix rows in the database, mainly because terribly slow, but it also requires a lot of code to loop properly within it's time constraints.
It was a pain to port Lucene to work on it's "filesystem".
Slow for what you pay.
Even MORE expensive if your app has spikes of traffic. My app has those spikes if a user that has many followers makes an action and we have to push notifications to his followers. Because of that I have to keep 10 inactive servers always on ($$$$$) to handle spikes.
Appengine isn't too bad due to the fact that I have the option to burn $$$$ instead of being concerned about scalability and fixing bottlenecks to reduce server usage. Sometimes it worth it.
My advice to people starting new products is to go with hetzner.de which is where I host my other products servers. It's cheap and extremely hackable. I have one server at hetzner that is handling 3x more traffic than the product that I have on appengine. The difference in price is $100 a month versions $2700 a month!
I have system admin experience, so the bottom line is that I would never choose appengine over having my own ROOT server. Don't be that bored software engineer wanting to experiment new things instead of building great products!