What do you like best?
Having an easy record of attempts at processing data, while also being able to clean it up for external consumption.
What do you dislike?
More of a Python problem, but it's annoying to have to restart the kernel to load changes in libraries, making things like the input/output number somewhat meaningless.
Recommendations to others considering the product
Great for projects where the data/experiment can be run on your own machine. I don't have experience with using the server format, but have seen people in my lab avoid Jupyter when it comes to running massively parallel operations on a cluster, in favor of vanilla Python.
What business problems are you solving with the product? What benefits have you realized?
I'm solving data science problems, often plotting data, exploring it, running experiments. In addition to the notebook format combining code and markdown, a couple great benefits are the tab-complete and built-in documentation for many functions, and being able to blend between an exploratory Python shell and a formal IDE.