He was very good about letting the people in his off site interviews explain their side, regardless of viewpoint. He was terrible about it in his in studio segments unless they were telling some harrowing story where he would obviously look like an ass for making a quip in the middle of it

I haven't seen his new show, but my understanding of the original is that they heavily edit the off-site interviews. This can create the effect that the guest is speaking uninterrupted and that the interviewer makes the guest look like a fool - but the effect is created through editing rather interruptions in person.

The new show was nothing like the old Daily Show. At least the couple of episodes that I saw of it.