What do you like best?
Wireshark is one of my favorite tools to analyse traffic and trace network, it save me lot of effort writing down my own parsers for dumpcap. I love the UI it is very helpful, the color coding, ability to filter streams, fetch the TCP packets and check content, dump it for later use. I use almost all these feature to trace and debug my application on low level networking that is almost impossible with my web browser.
What do you dislike?
However Wireshark is this useful, I have spent long time to learn and discover it, this is something I hated in the start, also sometimes I get stucked in the application trying to do some task that and it become very hard that at the I end I prefer to do it manually, this is not too often however, I thing if wireshark allows scripting this will be nice feature up there, and it will be my very favorite networking application.
Recommendations to others considering the product
Wireshark is your supporter in network tracing, this means you do need to know network before as it never assume you don't know what you are doing, don't mess with it unless you know what you do, or you decided to take the risk.
What business problems are you solving with the product? What benefits have you realized?
I use wireshark in tracing my network in case I'm working with socket inside my web application, it is easy to monitor network and dump capture files with it than using the CLI application that maybe not this usable.