Before the unannounced ArcGIS Online updates about a week ago, the following problems existed with the Web App Builder:
1. The problem mentioned above, that the Attribute Table widget would not show records. See error message.
2. Also, the descriptions on my domains were not recognized.
3. The Filter tool in the attribute table was unable to return to all records after being finished executing an initial query.
After the updates, now all of these problems are solved. It's very convenient that ESRI staff contacted this post after the unannounced updates to AGOL.