What do you like best?
The overall ease of use and simple implementation is nice. Intense Debate is easy to sign up for, easy to install in your WordPress site, and generally easy to get going. The fact that it leaves your WordPress comments in your local database, allowing you to migrate to another comment system in the future or disable Intense Debate entirely without losing your past comments, is also a great feature that was one of the deciding factors in using Intense Debate.
What do you dislike?
It's not actively worked on that much anymore. There have been a few patches, but it's not regularly updated and there's no new features on the horizon. The spam filtering isn't too great either, even with Akismet, spam comments regularly get through, especially from registered IntenseDebate users. There are some limitations as far as moderation and only allowing users to comment. We have experienced issues and heard complaints about problems with users trying to comment on mobile devices as well.
Recommendations to others considering the product:
Look at all of your options. IntenseDebate checks some of the boxes and is an adequate solution in some situations, but there does not appear to be a planned future, while WordPress itself and other comment system options, both in the form of 3rd party providers & fully contained plugins, continue to grow.
What problems are you solving with the product? What benefits have you realized?
Managing comments on any blog is a challenge. IntenseDebate provides adequate tools for the moderators and commenters alike. From a business perspective, being able to offload moderation to volunteer users and tapping into existing user management & authentication system is helpful. Like most WordPress plugins, the biggest benefit is in the savings of time and money to achieve the functionality that the plugin provides.