Wheel Base and Casters
The base of the best chairs will have at least five spoke bases. This will provide the best level of stability. Four spoke bases have a tendency to tip and lean. At best, a tipping chair can lead to an embarrassing moment. At worst, it can result in a painful spill and time out of work. Additionally, while most people move very little from place to place while in their chairs, high quality casters will glide smoothly across surface, again reducing the chance of a user tipping and falling.
A headrest is obviously designed to reduce the overall stress that the weight of the head places on the neck. Most people think this is a silly consideration, as their neck is constantly supporting their head, sitting or not. However, sitting means that every part of the back, spine, and neck are forced to support more weight then normal. A headrest is nice for most people and an absolute must for anyone with an preexisting neck issue.