Java Topology Suite

If you're looking for a way to visually check geometries, their validity, intersections and so on, the Java Topology Suite might be a very good idea.

It runs out of the box on Mac OS X (checked on 10.6.8) but you do have to run testbuilder.sh yourself (from the bin directory of the JTS distribution).

You can paste geometries out of postgis directly (by using st_asekwt and stripping out the SRID definition).
Just as postgis, it conforms to the Simple Features Specification for SQL published by the Open GIS Consortium so overlapping, crossing, and so on have the same meanings.