Does the Distribution represented by the training data need to reflect the distribution of the test data and the data that you predict on? Can I measure the quality of the training data by looking at the distribution of each feature and compare that distribution to the data I am predicting or testing with? Ideally the training data should be sufficiently representative of the real world distribution.
Over time, I realized that this whole issue falls under the umbrella of covariate shift which is a well studied area within machine learning. Link below or just search google for covariate shift. The concept is how to detect and ensure that your prediction data is of similar distribution with your training data. THis is in the feature space but in theory you could have label drift as well.