Bias in measurement, or systematic measurement error, can lead a researcher/scientist to favor the null when it is false or reject the null when it is true. These are, respectively, type I and type II errors.
Misclassification bias is a particular source of bias in studies, where study participants are wrongly assigned to exposed/diseased as opposed to non-exposed/non-diseased, that is their exposure/disease status is misclassified. This misclassification leads to bias in the results per se.
In a case-control study, misclassification bias can be eliminated largely if the same misclassification occurs in the two arms of the study, namely the case group (those that receive the treatment or intervention) and the control group (those that do not receive the treatment, or receive a placebo), because it balances and hence cancels out. This is called non-differential misclassification bias.
However, there is still a danger of misclassification biasing the results of the study if the misclassification is differential between the case and control arms (or more arms of the study if there are more than two). In this case the misclassification is not balanced out and the result may then be that the treatment appears more or less effective than no treatment or existing control treatments. Therefore, differential misclassification can bias the results of a case-control (or multi-arm) study towards the null (the treatment has no effect) or away from the null (the treatment has an effect).