UPDATE 8/18/23: FULL DATA FOR WEEKS ENDING 4/16/78 & 4/23/78 ADDED.
Below are the full weekly primetime Nielsen ratings results for the 1977-78 television season. Data comes from the Nielsen pocketpieces which were very graciously transcribed by an anonymous contributor. There are tabs available for each of the season's 52 weeks with the Household rating, share, and impressions available for nearly every primetime program. There are 5 partial weeks of the season where I am missing the associated Fast Weekly Household Report, so the data provided comes from a variety of sources including Newspaper lists, and trade publication articles. In those weeks, usually more half of the ratings data is available. Full rankings are available for each week except for July 2, 1978 and September 3, 1978 in which only the top 20 rankings are known.
This article previously only consisted of Newspaper scans to tell the story of this season's ratings, and those scans are still provided at the bottom of this article in case people want to see them. In some cases, the data in the Newspapers will slightly differ from the ratings in the pocketpiece because the newspaper data is based off of Fast National data while the pocketpieces are from finalized data. The pocketpiece data should be considered more accurate and the raw scans of them are all available under the "Pocketpiece" tab.
Below are the weekly Nielsen ratings results for the 1977-78 television season. Viewership wasn't reported by Nielsen until the fall 1988 season, so up until that point the only metric widely available was the household rating (which is what is reported here in this article). To calculate the estimated number of households watching, just multiply each rating by 729,000 as that is what 1 rating point represents.
Full weekly household ratings for every show weren't made available until 1981, so only partial results are available for this season. The first week of the season actually does have full results available, but the rest of the weeks usually only have ratings information available for the top 10 programs (from The Associated Press). Beginning with the w/e May 21, 1978 and through w/e Aug. 6, 1978 there are the top 15 results available (from from The New York Times). Unfortunately, there is no ratings data available for the w/e Dec. 18, 1977 or Dec. 25, 1977 - only rankings.
Additionally, the second document includes full rankings (without ratings) from both The Miami News and The Fort Worth Star-Telegram and these are available for most weeks of the proper season (not the summer) except for the following: week ending Oct. 16, 1977 (only top 10), Oct. 30, 1977, Dec. 25, 1977, Jan. 1, 1978, Jan. 8, 1978, and Jan. 15, 1978 (all only top 20). The final week of full rankings is w/e May 28, 1978.
ARCHIVED WEEKS (ratings - 51/53 weeks)
ARCHIVED WEEKS (full rankings - thru May 28, 1978)
Source: Nielsen Media Research via The Associated Press, The New York Times, The Fort Worth Star-Telegram, The Miami News, and Broadcasting Magazine