Pros
You can build customer service experience here in college (then leave to find a better "entry-level" position). Being a cashier here can improve your people skills. This job looks helpful or decent on a thin resume. After you're in the union (45 days), it is not easy to fire you. If you're in the right area you can work with some nice people. Some departments may be enjoyable (such as stock).
Cons
Kroger doesn't care about its employees. The union does nothing for people who actually do their job. Raises are strictly time based. Starting at minimum wage (new cashier or courtesy clerk), you get your first $0.10 cents raise at six months. After that your next raise is at a year. Praise is very scarce and little rules are often nitpicked (or encouraged to be by upper management). If you start as a courtesy clerk (bagger/cart boy) you have to beg for cashier, which would be fine if it functioned as a promotion but it sadly doesn't. After you're given cashier you get the next paygrade up in the union handbook (very likely ten cents). They can also make you a dual bagger/cashier. If you make supervisor you also get no raise. Vacation benefits and holiday pay are nonexistent until a significant amount of time at the company (over a year). Management is also abused and disconnected from their associates. Due to this disconnection, middle management (supervisors and leads) runs the show and are often incompetent because the only credentials they have are that they've been there long enough to require being given their turn at lead or supervisor.