What do you like best?
Mura is a full featured CMS, which is to say, it can handle the complexity of enterprise level websites. From user permissions to a custom page types, contact forms, multiple site administration, etc. It's modern, extendable, and has a really responsive team behind it.
It's CFML based, which might be a negative for PHP developers, but is a fantastic for CFML teams, because you can customize and extend it as needed.
I also like that it is a mature product that is still under active development.
What do you dislike?
Disclaimer; Users of the CMS would likely not experience these as issues; this is more from a developer perspective.
While reviewing the code, to see if we would be utilizing it internally, there were some design decisions, both on the front and back end, that we found questionable.
Additionally, like a lot of older, full-featured content management systems that were designed to handle a wide-range of use cases, the code felt bloated in places.
Recommendations to others considering the product
Unless you have experienced CFML developers on your team, make sure that you work with the BlueRiver team. They can provide excellent support and guidance. It's a great product; superior in many ways to Drupal, Joomla, Concrete5, and Wordpress. More features out of the box, nicer interface, great team behind it.
What business problems are you solving with the product? What benefits have you realized?
We were looking for a full featured, customizable, CFML based content management system (CMS). The end goal was building and supporting a fast, modern website, and making it easy for our content/non-tech team to manage the site.
While we ended up going in a different direction (custom, in-house CMS), Mura certainly does fit that description. It's a fantastic product.