I must admit I has been trying different apps like crazy, downloading games for my daughter, trying to side load Google Apps, trying if "officially" unsupported apps really cannot run, etc. So far it was pretty nice experience. If something does not work I simply removed it from device.
My first problem happen during when my Thanksgiving trip to Lake Tahoe in Sierra Nevada. Wi-Fi in hotel was slower than mobile connection. I got couple apps stuck in install in progress state. There is no way to stop it, uninstall them or re-download. When I returned home I tried to contact Amazon Customer Service but so far I could find a competent representative. Eventually they asked me to send logs from device. Guess what, their mailbox was overflown with emails and message was returned :-) As a bonus I learned that if you type ;dm in a search box it dumps logs to KindleLogs directory.
Another problem bricked my device for a while. I am using Kid Mode app which hijacks home button so kids cannot go out and do other things. It crashed and after rebooting I got blank white screen instead of Amazon Launcher. Again I had no lack with customer support call. They asked me to fully charge device, reboot and call them back in few hours. In meanwhile I figured out that if I kill Kid Mode app, release Home button from it I eventually got asked to choose default app to be associated with Home button. I chose Launcher and voila I am back. Good thing is that Kid Mode can reestablish child lock when I run it again so everything is back to normal.