The object of this note is to correct an error in the proof of Theorem 3.4 of the paper [An analysis of a broken P-1-nonconforming finite element method for interface problems, SIAM J. Numer. Anal., 48 (2010), pp. 2117-2134]. As a result, Theorem 3.4 requires a higher regularity than the usual elliptic interface problems can have, i.e., beta del p is an element of (H1/2+is an element of (Omega))(2) (0 < is an element of < 1/2). Hence we point out that even though the result now holds under this extra regularity assumption, the regularity is unlikely to hold for general interface problems. Thus the result has some limited usage.