I had a student job at the State of Illinois a long time ago.

From what I could tell their biggest problem hiring good people were:

1) pay rates tended to be well below industry, even when considering benefits (for programmers at the time)

2) their hiring process was really long. They had to go through this process where they had to find someone they wanted to hire and then get the req opened, which required apparently going through a lot of layers. It would take months and the candidate would find another job. Then they'd have to do it over again. I may have the details wrong, but going from finding a candidate they liked to giving an offer with a start date was multiple months.

There was also some other weirdness. Every time I logged into my computer it had this warning about everything I did being monitored. We were always lectured that anything we do could by FOIAed, and don't type anything that you don't want to be a headline the next day. They were also extremely strict about alcohol. There was a rumor in the office that on a student worker's last day his manager took him to a going-away-lunch and ordered a round of drinks. The student spilled the tea back at the office and the manager was fired the next day.

Overall in retrospect it wasn't a bad place to work. It seemed kinda oppressive to me as a student but in retrospect the environment wasn't bad.