The specimen question is really hard - I have seen such things that are to be sold (or also, really sold) which are obvious fakes, like the notes that had never existed, plus over-stamped with SPECIMEN stamp, but I tend to ignore such things (although sometimes I think of writing a warning on such garbage notes).
But on the serial numbers, there exist the specimens with valid numbers. E.g. with Bosnian Convertible Mark issue of 1998 (P-57 to P-70), which set I got from the Central Bank. These perforated specimens (the word "specimen" is made of holes) exist both with serial A0000000, as well as with normal serial number.
The note P-71 has only zero-numerated specimen, with added four digit specimen control number.