Recap: In dealing with bureacracies, the everyday person should avoid using logic or pleas for compassion at all costs and instead, realize that the Achilles heel of all bureaucracies is enforcement. I'm also using a tennisy metaphor for the bureaucracy (see previous post).
Here, it helps to look at things in a larger context and remember, if you're not Polish, that the system of enforcement here will have different weaknesses than in your home country.
In the US, generally, the best choice is to take a detail-oriented approach and make the line judge see that smudge on the line and convince them that your serve just barely touched the line. An alternative, is to take advantage of American phobias of confrontation and make interactions with you exhausting and unpleasant in hopes that they'll give you the benefit of a doubt, just to get rid of you (John McEnroe used this throughout his real tennis career, it didn't make him liked, but it was probably more effective than not).
Neither of these approaches work very well in Poland. On the whole, Polish people avoid attention to detail the way vampires avoid the dawn and relish the noisy confrontation. Foreigners lose most arguments in Poland, because their emotions too often get the best of them. Then they're labelled hysterical and ignored. (While arguing in Poland, volume and vehemence are fine, even encouraged, but you should never get so caught up in the heat of the moment that you can't share a joke or cup of tea with your opponent.)
What does work here? Several things, only a couple of which will be discussed here, but they all revolve around becoming a real person to the bureaucrat. If you can learn to argue in Polish (not just in language but in style), then go ahead. You don't have to be nice to be real. One of the enduring mysteries in Poland is how much more willingly people will do things for people they know and actively dislike than they will for people they don't. The flipside of this is how difficult it can be for people to work together when they agree about most things (see arguments between PiS and PO), but that's another topic.
Another method is to bring the lady at the desk some chocolate or something from the bakery. Not everybody can pull this off (I can't and don't try). If you do try it, it should seem spontaneous and not calculated and if you do it clumsily it will fail and get you labelled as a hopeless fool (in which case it can sitll work if you can inspire maternal feelings). I've never used the box of chocolate gambit myself, because I'm convinced I'd couldn't pull it off, I'd sound like I was saying: "Here's your BRIBE! Please, don't forget to take your BRIBE! Do you have your BRIBE now?"
And it's important to remember that this is not a bribe, you're not going to get a positive decision because you left some pączki on someone's desk or be denied because you didn't. The chocolates are a symbol (in a culture that relies heavily on symbols) that you've given a little thought to what might give the lady behind the desk a little pleasure. That is, you've made her a real person in your mind. Once you're done that, she'll often reciprocate.
There are limits as to what this will accomplish, it won't get you of trouble if your transgression is serious and it won't get you a positive decision if you've really screwed up. It can get the bureaucrat to use whatever discretionary power they have in your favor, so that if you missed the deadline by a few days (but not a few months) or it might get your application on the top or bottom or in the middle of the pile (whichever is of more help to you). It can also lead to a favorable interpretation of dubious information or take into account your motivations (if good) and overlook trivial mistakes. In other words, it can save you many frustrating trips to the same place and time and effort, freeing up your personal calendar for important beer drinking.
Is this corruption, I don't think so. All my reasoning (or lack thereof) will have to wait for another time, but I think the best argument is that the really corrupt do exist, and none the foregoing will work if you've come across a corrupt official (or a whole nest of them). In Poland, they especially cluster in anything having to do with cars (buying, registering, importing or driving them).Your only options are a) paying up b) working around them.