I found the CDN very easy to setup and configure within the Azure Portal.
Being Azure, there are plenty of free tools that allow you to manage the CDN from a UI that is not the portal. This was especially handy when I trained end users how to manage content within their specific realm.
The primary complaint I had with the CDN was expiring content once it was distributed. I realize it doesn't make sense for each endpoint to refresh content frequently, however if you upload something and need to make a tweak and then upload it again, you are kinda stuck. The only option at that point is to rename the content, which doesn't help if you've already distributed a link. It would be nice if you could upload new content to the source and force a refresh.
I would like to see more granular folder permissions. For instance, if I only wanted a single CDN but wanted to have folders for different divisions (marketing, hr, training, etc...) it would be nice to be able to get an access key at the folder level instead of the CDN level.
Content cannot be stored at the root of the CDN, you must have it inside a folder. This isn't a huge deal on a brand new setup but if you are moving from a prior CDN to Azure and already have content at the root, it makes that transition more difficult.
Cost-competitive: Azure CDN is very similar to other options from Amazon and Google, as well as smaller third-parties, and is priced to compete with those other PaaS vendors.
Like any solid CDN, helps alleviate load at origin nodes for static files.
A large number of points of presence means that many queries are already available close to end users, reducing the amount of time required to load most files as compared to loading them directly from the origin.