>He started his campaign with a pledge to "ban all muslims entering the US"
Half-truth. Trump isn't calling to "ban all muslims entering the US". Trump is calling for a shutdown of Muslims entering the United States until our country's representatives can figure out what is going on. There is a difference between the two.
>He started his campaign with [this pledge]
Half-truth. Trump started his campaign in June 2015. He made his statements on Muslim immigration in December 2015. This pledge came later.
>He has lied about seeing thousands of New Jerseyans celebrating 911
Half-truth. Lying is “a false statement made with intent to deceive”. Without looking into Donald Trump's head, it's very difficult to show there is intent to deceive. The most likely explanation I've seen floating around, is Trump saw footage of Muslims celebrating the attacks on TV, and mistook those celebrating for being in New Jersey.
NPR elaborates on why it's hard to call this lying here: http://www.spin.com/2017/01/npr-news-wont-call-donald-trumps...
>He has also said he "would certainly implement [a Muslim registry][1]"
Half-truth. In the article you cited, the actual quote is "Oh I would certainly implement that. Absolutely." But in the article you cited, it describes how it's not clear what Trump's "that" refers to. In his earlier answer, he says "There should be a lot of systems, beyond database, we should have a lot of systems, and today you can do it... But right now we have to have a border, we have to have strength, we have to have a wall. And we cannot let what’s happening to this country happen". In Trump's view, his "that" may refer to "a lot of systems, beyond database" plus "a border, [having] strength, [having] a wall". But if "that" refers to the reporter's question 4 sentences earlier, then "that" would refer to "a database that tracks the Muslims in this country".
The article you cited backs up this ambiguity, saying:
"The remarks were made after a rally, and there was speculation by some on social media afterwards that Trump did not hear the entirety of the question, because he refers to the border in his answer."
So really, what "that" refers to is ambiguous.
> the San Bernardino attacked was carried out by a US citizen of Pakistani descent.
Half-truth. The San Bernardino attack was carried out by two people, one of whom was a US citizen of Pakistani descent. The other attacker was born in Pakistan and immigrated on a marriage visa to the U.S.