Pros
Pay is decent and a pay raise is guaranteed at about the same time each year. I capped out after about 8 years and I've seen people do it in even less time. Take that in to consideration. Benefits are decent with 401k, Private Stock, Holiday bonus and insurance. Part time has guaranteed access to 401k and Private Stock after about 3 months I think but they have to get so many hours a year to qualify for the insurance the following year. Holiday bonus (2 weeks of pay) is only for Full Timers (and full amount is only given after 3 years of service). Meet some interesting people depending on your workplace and what kind of opportunities you try through Publix (like volunteering and/or going to store openings). College scholarship/financial aid opportunities. Learning experience in general.
Cons
Your coworkers and/or management will make or break your workplace environment just like any other job. They WILL promote idiots or suck-ups. I've met plenty of people who are good people but BAD managers. As the years have gone on, they've taken more and more away from the employees (especially those who are NOT in management). Bonuses for inventory aren't available anymore unless you're in management. And even then it may only be for the department managers (not assistant managers) but I'm not 100% certain on that one. If your store has overnight grocery, a lot of blame is put on them for "not getting enough done". Slacking off is becoming more prevalent (at least in my department of Grocery). There's a lot of "That person's getting away with not trying as hard, so why can't I?". There's no proper repercussions for said slackers. Management will sit down and have a chat, yes, but the issue isn't truly fixed because the person just goes back to it. This may all be completely dependent on your manager though. They will lend out people to other stores even when your store may be hurting on people. So good luck during those days/weeks.