Aristotle believed that an ignoratio elenchi is a mistake made by a questioner while attempting to refute a respondent's argument. He called it an ignorance of what makes for a refutation. For Aristotle, then, ignoratio elenchi amounts to ignorance of logic. In fact, Aristotle goes so far as to say that all logical fallacies can be reduced to what he calls ignoratio elenchi.
Modern use limits this term much more narrowly to the kind of mistake described in the first paragraph above.
Maher: It's arbitrary, isn't it? If you had been born in Pakistan, you wouldn't be believing in Jesus Christ. You would have been told another fairy tale and you would have been believing that.
Scarborough: Well, Bill, that's your opinion.
Whether Maher's argument is his opinion or not is irrelevant and does not address the argument made.
The conclusion is ignoratio elenchi, since friendliness and charity are not the main qualifications for induction into the Hall of Fame.
The existence of worse criminals is a secondary issue which has no bearing on whether the driver deserves a fine for recklessness. If the speaker were deliberately attempting to divert the issue, this would be an example of a red herring. While the argument about how the police should spend their time may have merit, the question of whom the police should prioritize pursuing and the question of what should be done with those the police have caught are separate questions.
A red herring, the unrelated alleged affair, attempts to change the subject away from the popular policies. However, if the original discussion were of the prime minister's public integrity (encompassing both popularity and conduct), this argument could be perfectly valid.