This is a reduced relative clause. The full versions are: The interview, which was broadcast live across the nation the other day, attracted large numbers of viewers. The interview, which was broadcast live across the nation the other day, attracted large numbers of viewers. So the first one would only be used if you were going to describe an interrupted action. The interview, which was broadcasting live across the nation when the incident happened, attracted a lot of controversy. So the second one is correct. In general when you have a reduced relative clause, you can make it a simple sentence to check which one is correct. The interview was broadcasting live across the nation the other day. The interview was broadcast live across the nation the other day.

"The other day" hints that it is something that happened a few days ago So, continuous " broadcasting " is unlikely. I would say "broadcast."

2. The interview, broadcast live across the nation the other day, attracted large numbers of viewers. The above is the correct rendering because it allows for the grammar to communicate that this event already happened in the past when you add the 'other day'. Unlike the first rendering which uses the continuous form of broadcast-broadcasting which communicates that this event is on-going for a particular time