Or at least it was a much more realistic portrayal than mafia movies had been in the past. They had mafia consultants on set, and there was a great deal of research that went into the movie. It is a much more realistic mafia movie than many of the other movies since as well.
Yes, the Godfather accurately portrayed the Mafia, because it tells the story of the power and control and the bullying on the streets that the Mafia uses. Even without the name, everyone knows that the Godfather was telling that story. They were still able to portray what the Mafia does in a convincing way.
Mafia is ruthless and it ruin lives. Any portrayal of mafia in a light that one of the criminals involved have any honor or pride is wrong and it greatly dismissed and disrespects the victims of mafia across the world. Being someone who has lived in Italy for many years, I guarantee you that there is nothing honorable about being in mafia.
I think the Godfather focused a lot on the internal family conflicts and left out how damaging the mafia was and still is to society. It accepts the mafia as a part of society and in a way shows that we all only care about ourselves. It's a masterpiece, there's no doubt about that, but it doesn't paint an impartial portrait of the mafia.