I often hear people throw around the term tircha d'tzibbur, that something being done is incorrect because it is a burden to the public or congregation. Usually I hear it being used for whatever assaults the personal preferences of the person invoking it. Is there any objective definition of what violates this rule?
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This article has a fairly detailed explanation of Tircha D'tzibbur. It discusses various places where this is mentioned in the Gemarrah, and which halachot apply as well as practical applications.
In summary, according to the article, Tircha D'Tzibbur is an extension of "Ve'Ahavta L'Re'acha" - loving your fellow. I.e. - if you are commanded to love one person, you are certainly commanded to love and respect an entire congregation of people (tzibbur) so you would not do anything to "burden" them. What constitutes "burden", I think, is well defined within the article and its linked sources.
In summary, the judgement of tircah d'tzibbur is not based on one's person preference of "what I don't like". Rather, it is based with a thinking of others, essentially placing the congregation or public's needs before yours.
This is why the article states that someone should not park their car in a bus stop so that it blocks the bus from going into the bus stop and having people load and discharge in the middle of the street.
I would add to this list a prohibition of parking in a handicapped spot when you are not handicapped. Besides being a tircha d'tzibbur (mind you a "subset" of the general population, but, nonetheless, a "tzibbur") there are probably other violations involved in this action.