Internal validity is important for RDD inferences. This validity has to satisfy two assumptions, namely:
Assumption 1: Imprecise control of assignment around the cutoff. Individuals cannot control whether they are just above (versus just below) the cutoff.
Assumption 2: No confounding discontinuities. Being just above (versus just below) the cutoff should not influence other features.
It becomes a problem when these assumptions are violated. For example, the moment participants can control, manipulate or predict whether they are above or below the cutoff then the randomness of the cutoff point is compromised rendering the RDD internally invalid.
The other assumption makes sure that everything else is fixed/constant and the cutoff is the only discountinuity.