In [9] the notion of weak partial congruence algebra is introduced and, among other things, three problems are posed. In the present paper we give the complete solution for the first problem and some partial answers for the second one. Also, we prove that there are modular algebraic lattices which are not representable as the lattice of weak congruences of any congruence permutable algebra. This fact solves Conjecture from [10] in the negative.