My wife stumbled upon a case recently in which the DC Superior Court ruled that paying a civil fine for a traffic ticket by mail is inadmissiable in a related civil action. This is different in than a formal plea of guilty to a traffic offence, which is admissable. (See Frost v. Hays, 146 A.2d 907, 908 (D.C.1958)).
They further point out that
Many courts have considered the precise issue whether payment of a traffic fine may be admitted as evidence in a related civil case. Virtually without exception, such evidence has been deemed inadmissible. Within the past decade or so, the Supreme Judicial Court of Massachusetts, in ruling on the issue, cited, merely as examples, no less than nine such holdings and stated that it had found “no case to the contrary.”
They also note that the fact that one is ticketed is also inadmissable. It constitutes the opinion of the police officer making it hearsay. The officer would need to come to the trial and be available for cross-examination for mention of the ticket to be admissable.
So if you get a ticket from a cop and they're wrong, it doesn't screw you in a civil case, even if you pay the ticket.