Qualifications
Regardless of your exact position within the DMV, the most important qualification for this line of work is the level of shenanigans and negativity you can deal with on a regular basis. You're working at a place of business, providing a service, and helping customers through issues.
Each position is going to require different experience and knowledge. Some jobs only require a high school diploma and entry-level skills. For instance, the person at the front desk needs to deal with the daily level of ugh-inducing, eye-rolling moments with customers, plus data entry and cash handling skills.
Other jobs will require advanced skills, sometimes even a degree to go with them. The IT professional needs to be good with computers and their out-of-date systems—states aren't exactly chomping at the bit to fund brand new computers at the local DMV. Inspectors need the analytical skills and interviewing abilities to determine fraud, fault, and everything in between. There are jobs for everyone at the DMV, so know what you're good at before you apply for the wrong thing.