Due to Quantum Theory alone, "literally no chance" of anything becomes impossible... let alone factoring for human error.
However, the process is all pre-sealed individually packaged health products administered by professionals who are adequately sterile and protected.
There are some infinitesimally small chances for cross-contamination which could be considered nearly negligible. I wouldn't be worried about it at all.
The things you should know are that, yes, it will scar. In addition, on a rare occasion someone new, or inattentive will poke you and have to move the needle or insert it into the other arm. On a very rare occasion, approximately once every couple of years if you go consistently, blood may be inserted outside of your vein into the soft tissue of the arm. This will cause pain, followed by about two weeks of discomfort and bruising. During which you will not be able to donate. In only one documented case which I found as I researched, has this lead to a more serious condition.
Overall, nothing to worry about. A few scars, minor discomfort, and making some money to save lives. To be honest, if there weren't some discomfort or time spent, they wouldn't pay you for it... most people would do it for free.
Hope that helps.