What do you like best?
This tool is great for allowing anyone already familiar with PowerPoint to convey reasonably simple and short content asynchronously. It's quick and easy to learn how to use it and even allows for some basic types of quiz questions. You can publish it to your company's Adobe server (if you have one) or as a SCORM package to upload to a traditional LMS. It gives you the choice of recording audio within its own PowerPoint ribbon (not my method of choice) or to import and sync audio created outside of Presenter (which I prefer, because it's easier to edit and maintain.)
I also love that it comes with Adobe Presenter Video Express, which can be used within the Presenter ribbon or as a stand-alone application. It's a very easy way to create short system demos with narration, and allows for zooming and panning, as well as allowing you to intersperse, or even simultaneously show, webcam video.
What do you dislike?
I don't know if this qualifies as a "dislike," per se, but it's important not to try and use this as a full-fledged e-learning authoring tool, as the opportunities it affords for effective practice and feedback is minimal. It's a well-named product, since "Presenter" really is best used for "presentations," rather than bona fide training. There's no real "programming" ability (like being able to use custom actions and variables). I also wish that, when syncing animations to audio narration, if you make a mistake mid-way through a slide, you could re-do just from where you made the mistake on forward, rather than having to resync the whole slide. Also, better audio editing capabilities within the product would make it less necessary to use an external audio editing product.
Recommendations to others considering the product
I should add that it also can publish to a mobile-friendly format, for those who need that feature.
What business problems are you solving with the product? What benefits have you realized?
This tool is best used when what you're trying to create is the online version of someone getting up in front of a large group and making a presentation (rather than trying to do real "training"). As such, we've used it to announce new product features or give general overviews of new products (to be viewed as "pre-work" for an upcoming training session), do short overview demos of new systems (more of a "here's what it can do" than "here's how to do it," although it could be used for micro-learning, if the tasks are very short and simple), and to convey some basic on-boarding info.