What do you like best?
Mendix takes a lot of the guesswork out of building business applications. They have a very solid framework for creating efficient databases, integrating with the databases and building various workflows (using microflows) to enable users to accomplish their goals. The app builder (Modeler) is very intuitive and makes it quite easy to visually prototype an app, gain agreement, then fully code the app. This process does not require a traditional, highly-skilled developer to get started.
In addition to the development environment, their cloud hosting is also extremely convenient and quite worry-free for most applications.
What do you dislike?
What I dislike is less about the technology and more about the challenge it is to find developers with Mendix experience. While there are millions of Java or .Net developers in the world, there are thousands of Mendix developers. They are hard to come by and when you find them, they're costly. So what you might save in rapid development, you give (at least somewhat) in resource costs. Over time I would expect that to get better.
Recommendations to others considering the product
Before jumping in, test it out an a very specific, small, time-bound project. It's easy to do that and will give you a real feel for what you should experience in the future. If you have in-house development staff, they will likely be apprehensive about Mendix. However, business stakeholders will love the ability to "see" the process unfold before their eyes.
Mendix can't solve every problem so be sure it's right for what you're trying to accomplish. If you have a focus on improving business processes, then it could be an amazing fit. If you're trying to integrate disparate systems, it could also work well. If you're trying to build a consumer-facing website or portal, there may be better solutions that will cost much less and get you there faster. So know what you're trying to do and see if it works.
Last thing, it will be a culture change and you have to be ready for change management.
What business problems are you solving with the product? What benefits have you realized?
We have mainly been focused on building internal applications to improve and automate various business processes. In some cases the ROI is around needing fewer people to handle an increased workload (first application resulted in a 3x productivity gain). In others, the result is eliminating n external vendor application that was simply not integrated into anything else (reducing multiple-entry situations, increasing data quality, eliminating licensing costs). We've also found that we can be much more nimble with turn-around, nor only related to reduced reliance on external vendors, but with development cycles that are typically based on 2 week sprints.