During the ending credits when Lisa is running after the kid you can clearly hear the shoes smacking against pavement or a hard floor, though they are supposed to be running around the White House lawn.
Beth: It's ironic. Like when it rains on your wedding day.
Beth is referring to the Alanis Morissette song Ironic which contains many different situations, none of which are actually ironic.
Jimmy James: Well if you keep up that attitude you're going to get your you know what caught in a big fat wringer.
This is an reference to when John Mitchell (then currently under the Nixon White house) called Kay Graham of the Washington Post, and said to her that she was "going to get her tit caught in the wringer" over the now famous Watergate story. In addition just moments before Jimmy James makes a veiled reference to him again being deepthroat.
Joe: I don't know how to tell you this, but there is a spunky redhead in every office.
Beth: Tell me about it.
This was a dig at the show Suddenly Susan which also appeared on NBC, but debuted a year after NewsRadio. Many of the people on Newsradio felt that Suddenly Susan's spunky red headed outrageously dressed secretary character Vicki played by Kathy Griffin was a direct copy of NewsRadio's spunky redheaded outrageously dressed secretary Beth played by Vicki Lewis. Certainly the coincidence of the names is suspicious. By the way, notice that the office upstairs also has a spunky outrageously dressed redheaded secretary.