- The characters Niles and Daphne in "Frasier (1993)" have a child named David, which is named in tribute to him.
- On Frasier (1993), the show's featured radio station KACL 780 AM was concocted from the first letter of each of the show's producer's surnames: David Angell, Peter Casey, and David Lee.
- He wrote ten episodes of Cheers (1982) and won an Emmy for an episode that first broadcast on November 17, 1983 titled Old Flames (1983).
- Before turning to writing for television, he worked as a methods analyst at an engineering company and then at an insurance firm in Rhode Island.
- Served in the army and at was stationed at the Pentagon in Washington, DC, in 1972. On Sept. 11, 2001, Arab terrorists hijacked three jet airliners. One crashed into the World Trade Center in New York City, and another crashed into the Pentagon, where Angell had worked. He and his wife Lynn were passengers on the jet that crashed into the World Trade Center and were among those killed. They were returning home to California after attending a family wedding in Cape Cod, Massachusetts.
- In 1994 he received an Honorary Doctorate from his alma mater, Providence College. He received a Bachelors degree in English from Providence College in 1969.
- He was the son of Mae Theresa (Cooney) and Henry L. Angell. In David's script for "Archie Bunker's Place" (1979), parts of the episode took place in a store called "Henry's" which was named after his father.
- He is said to have coined the word "boink" to mean sexual intercourse.
- Formed Grub Street Productions with partners Peter Casey and David Lee.
- Entered the army upon graduation from Providence College and served at the Pentagon until 1972.
- His brother was the Roman Catholic bishop for the archdiocese of Burlington, Vermont, USA.
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