I had a bit of a problem leaving the country last year at Ezeiza.Basically, for a few minutes they weren't going to allow me to leave because I didn't have my DNI. Although I have the permanent resident stamp in my passport they asked for my DNI as well.
I explained or I should say my wife explained to them my application was waiting to be processed.The officer said I should have been given a temporary document detailing this.
Finally after about twenty minutes and much nail biting by me he returned after consulting a superior saying that it was okay for me to travel. I have to say he was very polite and understanding about the whole thing but it did seem strange how a foreigner could be prevented from leaving another country.
Nine months after submitting my DNI application it has been sent back to me because it was missing a signature, not by me but the registrar who dealt with me.