No, what it does is to prove that the cops were lying about several things.

At the time of the exchange, there was one disinterested-looking bloke who was too far away to hear what was said. After Mitchell had gone, several people appeared to gawp through the gates.

Although there's only the word of the cops against Mitchell using the offending word and his word that he didn't, the conduct of the cops was so bad that four were dismissed from the force and one other was jailed so in the circumstances surrounding the affair, in the light of the proven misconduct, a jury (should such a case have gone that far) would (should?) be more inclined to accept the word of Mitchell than a bunch of proven liars!