They are commonly called mixed pixels or mixels. Topology is the property that describes adjacency and connectivity of features. A topology data structure encodes topology with the geocoded features. Topology allows a GIS to do error correction. Topological functions allow the elimination of slivers and the use of fuzzy tolerances.
Topology also allows adding raster-like attribute data to a vector data structures.
An advantage is that overlap areas are cleaner and redistricting is easier. However, reconstruction of features require complex software, especially small features. Database Management Information versus Data. Information is the act of making sense or meaning of data. Data can be just numbers.