What do you like best?
I like the absolutely massive range of applications that Powershell can interact with and manage. Everything from Windows to the Exchange Cloud to SharePoint to Active Directory is fair game for Powershell. If it doesn't do it out of the box, there is probably a cmdlet extension of plugin that can give you the functions you're looking for.
What do you dislike?
I wish that the Powershell shell program came with the Office 365 cmdlet packages already installed. In the very cloud focused world nowadays, I am surprised that we don't already get the O365, Exchange, and SharePoint modules by default in Windows 10 Pro.
Recommendations to others considering the product
There are a ton of online resources for Powershell. I would head to third party resources before tapping any Microsoft direct help sources. The Microsoft direct sources always seem to have some trouble. To make up for this, there are many highly active communities online.
What business problems are you solving with the product? What benefits have you realized?
We administer parts of our Exchange, O365 and SharePoint environments with Powershell. We also utilize Powershell for some unique active directory activities.