First of all, Pinocchio's nose growing is original to the Italian book and its very unlikely that it was intentionally anti-semitic. Its more likely a phallic image but in all honesty it was probably chosen as a way to physically show the morality of Pinocchio's decision. Many forget that the character of Jiminy Crickett is very small in the book and the theme of morality and choices needs a way to be seen.

If you are looking for an anti-semitic character, Stromboli is far clearer. But even he is a mix of Jewish and Italian stereotypes.

Many characters in shorts or side-characters are stereo and archetypes , this goes back to the days of Commedia Dell'Arte, Punch and Judy, and medieval morality plays. When you have such a short time to introduce characters and, in the case of most cartoons, their purpose is for broad comedy, you tend to use these typecasts. During the time the audiences would view them as being Jewish, or black, or Italian, and some would definitely find them offensive. But most wouldn't, as time has moved on the sensitivities of the audience has changed. Racial stereotypes like The Mammy are now seen as reprehensible because of America's history with black face, slavery,and the black power movement. You can still see stereotypes in media, but they are not the same as those in the 1940s.