I was pulled over by the cops (in Chutz la’aretz) for speeding. I was wearing a Kippa and had visible Tzitzit. The officer could tell my religion. I was very polite and courteous, ever mindful not to give a bad impression (he still booked me though). Have I made a Chillul Hashem by breaking the speeding limit and being pulled over? If so, how can I rectify this specific error, and how can one rectify a general Chillul Hashem?
The notion of Chilul Hashem does apply in regarding to non-Jews whenever they are expecting better behavior from the Jew. [see Tosfot Bava-Kama 113b] If it is a common traffic violation that most people may transgress and is understood [even though not forgiven] by the authorities and Jews are therefore not looked upon more than others in a bad way – such case may not be defined as Chilul Hashem. In the case of a serious infringement where most people are expected to obey and the Jew is looked upon as one that should present higher standards of behavior – it may fall into the definition of Chilul Hashem. Complete Tshuvah for the classic Chilul Hashem is not always a simple task and in extreme cases almost unattainable [see Yoma 86a] Your case on the other hand seams as a light case of Chilul Hashem if at all, as mentioned above; in such case I believe the words of Rabenu Yona in his Sha'arei Tshuvah [4; 5] that one should increase Kidush Hashem i.e. sanctifying Hashem's name by acting meticulously appropriate in that regard, are to be applied.