The dialog that comes up when running Open(), or Pick File(), looks exactly like a standard File > Open dialog (at least in JMP 9 on the Mac) but it seems to be limited. In contrast to the standard open-dialog only one file can be selected in the open-dialog called from JSL.
In Mac OS X I haven't found a way to open the standard dialog from script, but it may be possible on Windows where JMP can call dll-files. I am not of much help in that area but there som amazing examples in other threads of what can be done via dll.
If you would find a way to do that, the code below can be used to get a list of the names of the last opened data tables.
nr_of_already_open_tables = N Table;
Open( );// some clever dll funcion or similar
last_opened_tables = Local( {i, d = {}},
For( i = 1, i <= N Table() - nr_of_already_open_tables, i++,
d[i] = Data Table( i ) << GetName
);
d;
);