Reusing data used for making prediction for training I wanted to understand and make sure that the following way of making predictions and training model is correct:
I have a model $M$ and it makes a prediction on data $X$ today, tomorrow the model retrains and in training data it will include the yesterday's data $X$ and so on.
Is there anything that could be wrong with this approach, I know that the other way is wrong i.e. I should not use the training data for prediction but is the vice-versa also wrong.

No, there is nothing wrong if you can handle the computational expense introduced by frequent retrainings. This doesn’t introduduce data leakage.
