There were a couple.
A big issue came up with user change. Not many users like to change their day-to-day activities.
There was also the major issue of thin clients versus thick clients. Installing thin clients is ideal, but, you end up with a lot of E-waste afterwards to dispose of, or re-use, or store.
Another challenge was network performance. Many users connecting to our VM infrastructure needed to be taken in to account. Switching, routing, and bandwidth management were a must.
Another challenge was memory management on the VM infrastructure side. Power users should be put on to a host with more memory than the other users.
All good things to look at when going with VDI, or any virtual desktop implementation.