Who knows, maybe he has changed his appearance ?
Unfortunately, I don't know how they recruit Police officers in Japan to answer your question correctly, could it be that there are more than one Police Academy ? How big is the one Date attended anyway ? Takagi and Date probably didn't attend the same one, because he only heard that Date was the first, but in fact he was just a second (and Date is only one year older than Takagi, so we can assume that they both studied to become police at the same period of time).
I'm also not sure if there exists such a thing as a real ranking system in the school, so it doesn't necessarily be that Amuro had to be very popular (I hardly know who the hell is the best student in my university, and I don't care about that either; so I guess in Conan it's also the same, people don't take such things very seriously). Especially after all these years, I don't think much people would remember his face (assume that they have once heard of him).
By the way, I don't see much the problem of someone recognizing him. If the other purpose he mentioned was to find Date, then people would know that anyway. I don't think he's afraid if someone knows him. He doesn't do anything illegal to hide, does he ? *cough* *cough* *cough*