Finding geometry anomalies using ArcGIS Pro

Have you tried Geo-processing tool in ArcGIS https://pro.arcgis.com/en/pro-app/tool-reference/data-management/check-geometry.htm

This checks any errors or invalid geometries in the dataset and reports into a file.

Hope you are looking for this.

Let me know if you are looking anything specific with an example.

As it stands I think your question may be too broad for focussed Q&A because it seeks techniques for identifying multiple anomalies in your data.

If you want to identify any polygons in your data which are not "nice rectangles" the technique I would use is to write an ArcPy script using a cursor and the @SHAPE token to examine each polygon geometry to:

1. Count the number of parts and rings
2. When there is only one part and ring count the number of vertices
3. When there are five vertices (the last to close the polygon back in itself) create a list of lengths for all four segments, applying whatever rounding rule you think is appropriate, and calculating a set of unique list values.
4. When there are two unique segment lengths calculate the angles between each adjacent pair of segments
5. If the angle between each pair of segments is close enough to 90 degrees (for your purposes) then you have a rectangle, unless two of your vertices are coincident (within your tolerance).