Noise in the data, to a reasonable amount, may help the network to generalize better. Sometimes, it has the opposite effect. It partly depends on the kind of noise ("true" vs. artificial).
The AI FAQ on ANN gives a good overview. Excerpt:
Noise in the actual data is never a good thing, since it limits the accuracy of generalization that can be achieved no matter how extensive the training set is. On the other hand, injecting artificial noise (jitter) into the inputs during training is one of several ways to improve generalization for smooth functions when you have a small training set.
In some field, such as computer vision, it's common to increase the size of the training set by copying some samples and adding some noises or other transformation.
