What do you like best?
I like that any.do has a pretty seamless interface across platforms--I use it on both desktop and iPhone and things seem to flow well between the two and not get lost. The interface is similarly easy in both places, too. I also like the automatic addition of my Apple Reminders as their own task list.
What do you dislike?
any.do doesn't integrate with my calendars, either Outlook or Apple, so it doesn't do everything I need in terms of date-sensitive planning. It also doesn't function for cross-team work planning, as it's a single user interface.
Recommendations to others considering the product
If you are looking for a basic, easy-to-use, easy-to-sync task list application, I have tried a large number of them, both free and paid, and any.do is just about as good as it gets. If you need something more robust, with calendaring and/or sharing functions, you should look elsewhere.
What business problems are you solving with the product? What benefits have you realized?
The problem I am solving, both personally and professionally, is simply keeping track of tasks and sorting them into lists. And for that simple need, with a clean, easy-to-sync interface, any.do is about as good as it gets. It's more complicated functionality that requires me to use other tools.