What does it matter if he "happens to carry a gun"? Is that really the first place your mind went? Its not like he is saying "lets go for dinner. Oh, did you see my gun?". An officer's sidearm is a tool of the job, and its responsible use sacred and respected. Is is a threatening tool? Yes, but only when it is drawn. All cops hope and pray they will never use it in their career (and most never will). Why should you, a (presumably) innocent civilian have any reason to worry about his gun?
Do I personally find this to be cause to FIRE the cop? Absolutely not. What one of us out there has not made a stupid decision because of an interest in someone? Cops are people, and people make mistakes. We should and do hold them to a higher standard, but in this case nobody was hurt. He did not make use of any information in addition to that which he obtained at roadside, so to me there is no evidence he "looked up her records" at all. Your license has your address on it. The cop left a note on her car. This does not constitute stalking (that requires repeated behaviour), and also does not constitute a threatening action.
What I find to be the most bizarre matter in this case, is how the plaintiff has chosen to go public with this, and all her information: Her name is Evangelina Paredes, of Kendall Co, Illinois. Shes a single mom, with "nobody home to protect her". WTF?? They just took a controlled situation (one identifiable cop who made a mistake with some entrusted information), and gave that exact same info to the entire world, including all the creepers and stalkers in Chicago. Ms Paredes and her lawyer have now opened her up to significant threat, especially if she wins this lawsuit with a nice payday.