As soon as an error has been done, we may want to have a feedback: "you have made an error!". This feedback could be a sound, a visual signal on the screen, or anything else that could indicate to the player that what he played just before was wrong. This cannot be done for everykind of errors: dynamic errors, for example, need a large "window" to be detected, and a real-time indication like "you have played too loud" would not be relevant.
For didactic purpose, it would be a good idea to indicate errors immediately: the players know what he just played, and doesn't have to remember "what did I do meas.37 ?". But the related problem would be the following one: it's sometimes difficult for a beginner to stop and then continue to play from a given point in the score. Moreover, a real-time signalisation could definitely disturb the player, and make him do much more errors because his attention has been distracted.