With the line employee, I like to develop a rapport first if there is time. I've found jumping in and helping do the work helps to learn what they do, the challenges they have, etc., and gains some respect from the front line. You may even appear to have credibility ;-). Helping with the work is not possible everywhere, e.g., many union shops.
To whom to address the issue. If there is no set rules for this, I typically start with the individual. Most of the time it is a training retention issue where a quick reminder is enough. Then up from there, but I do not skip levels - going over heads can fan the flames of a blame culture.
Food safety issues - when and how I address is guided by risk. Someone leaving a torn bag of mustard flour (an allergen for us as we export), with forklifts driving through it in the warehouse remote from the production area is egregious, but it is not an emergency. I do not know who did it, so a talk with the warehouse manager at the next meeting is in order. If I've got time, I'll clean it up myself.
Someone picking up a fallen, unpackaged ham off the floor and putting it back on the line in an RTE facility is egregious, and it is an emergency. The line must be stopped and cleaned. Management by virtue of the situation is involved immediately.
Someone not wearing their beardnet over their mustache while boxing enclosed product - not egregious. This can be addressed to the individual, reminding him of the GMPs in the training. If he refuses and it is not addressed, this becomes more urgent as others will see that beardnets are no longer required.
A general thought or concern goes to my boss or I bring it up in our HACCP team, but I do not express those on the production floor.
Not sure if I got at what you're asking but those are some of my thoughts.