Pros
Management, at least at my location, are fairly supportive in allowing days not available not to work. They also are more willing than other places I've encountered to give you slack when you need it most depending on the circumstances. I don't even consider myself a "favorite" and I get that treatment. Its very hard to get fired at Publix, you have to do something big and down right bad to accomplish it.
Cons
The pay is below average in all departments. Its more than Kroger but thats not saying much. Opportunities for quick advancement are limited. The downside to Publix is that they retain too many people in the departments, this overextends the hours available making it hard to make a living if you're part time. The current raise increment is 15 cents for an above average evaluation, used to be 25 cents. Publix has had instances where it has rehired members of management who acquired a misdemeanor conviction stealing from their own store location.