Pros
Working in a museum setting and in a beautiful building designed by a famous architect. As part of Yale, there are many benefits such as job security, free healthcare, lots of time off, etc. (Despite the cons, the benefits at Yale are what keeps most people working at Yale).
Cons
If you're not one of the curatorial or scholarly employees, then you're pretty limited in terms of job advancement. You can spend years working here and never be offered a promotion or increased responsibility, despite being worthy. Administrative staff don't see the same perks or earn the same respect as their curatorial/scholarly counterparts. External expertise is overvalued; internal expertise is undervalued. Management lacks trust in employees. Also, resistance to trying new methods of doing things. Too many meetings.