What do you like best?
The online community (IRC, forums) is a great place to learn. The users are extremely helpful and nice.
KV language is great. Kivy is great for building a cross platform application. Easy to port to android.
What do you dislike?
A little tricky at times to get the event dispatching and property bindings right, but once you understand it it becomes very powerful.
Recommendations to others considering the product
It is a great new platform. It can help you create amazing cross platform apps and it's framework is very flexible and robust. It will not, however, create native looking applications. With a little time and effort you can make the application look native.
What business problems are you solving with the product? What benefits have you realized?
Cross platform application development with main focus on embedded linux and android. It was very easy to build the app for both linux and android. There was no differences in how it ran under each OS.