JOSM - is it possible to copy data from the "Suspicious data found" dialog?

If by "copying" you mean "put in the copy-paste buffer", then it seems to be possible at a basic level:

• Get the dialog to appear or even use the validatior tool in the sidebar
• Open all branches of the tree using the mouse
• Type Ctrl-A to select all and Ctrl-C to copy
• Open your favorite text editor and type Ctrl-V to paste

It returns something like

Warnings
Crossing buildings (1)
TestError [tester=org.openstreetmap.josm.data.validation.tests.CrossingWays@7a48772, code=601]
Building inside building (2)
TestError [tester=org.openstreetmap.josm.data.validation.tests.BuildingInBuilding@2f6d8855, code=2001]
TestError [tester=org.openstreetmap.josm.data.validation.tests.BuildingInBuilding@2f6d8855, code=2001]
Unnamed ways (1)
TestError [tester=org.openstreetmap.josm.data.validation.tests.UntaggedWay@2636111d, code=303]
Way end node near other way (1)
TestError [tester=org.openstreetmap.josm.data.validation.tests.UnconnectedWays@5c0b646d, code=1301]
Crossing ways (4)
TestError [tester=org.openstreetmap.josm.data.validation.tests.CrossingWays@7a48772, code=601]
TestError [tester=org.openstreetmap.josm.data.validation.tests.CrossingWays@7a48772, code=601]
TestError [tester=org.openstreetmap.josm.data.validation.tests.CrossingWays@7a48772, code=601]
TestError [tester=org.openstreetmap.josm.data.validation.tests.CrossingWays@7a48772, code=601]
Other
A name:* translation is missing. (1)
TestError [tester=org.openstreetmap.josm.data.validation.tests.NameMismatch@30de03a5, code=1502]
...etc

Which is only mildly useful. This works for me, JOSM 6232 on Linux.