First of all, thanks for pointing out that there are new banknotes. I had already wondered whether there would be Trichet-signed notes or not. I personally haven´t seen one yet.
The 2002 is not the year of issue or printing. It´s part of the copyright notice. For example, I have a German banknote in front of me, the penultimate series which was in use from the sixties through the early nienties: besides the issue date on the front (Frankfurt am Main, 2. Januar 1980, accompanied by the signatures) there´s a small "(C) DEUTSCHE BUNDESBANK 1963" on the back. Same case as with the Euro notes.