Known group key transfer protocols in group communications using classical secret sharing require that a t-degree interpolating polynomial be computed in order to encrypt and decrypt the secret group key. Secret sharing plays an important role in ensuring the group communications security. A verifiable multi-secret sharing (VMSS) scheme is a multi-secret sharing scheme with the verifiable property. Recently, Zhao et al. and Dehkordi et al. successively proposed two threshold VMSS schemes. Shortly, using the same verification mechanism, Dehkordi et al. presented another two VMSS schemes. In these schemes, authors claimed that the dealer was absolutely impossible to become a cheater. In this paper, we show that in both Zhao scheme and Dehkordi scheme, a dishonest dealer may distribute a fake share to a certain participant, and then that participant would subsequently never obtain the true secret. Indeed, verification mechanism should be improved in these schemes; and furthermore our results highlight that extra cautions still be exercised when constructing schemes in this direction.