Logical OR operation in a homomorphic additive cryptosystem
Well, the problem is with logical OR and subtraction (which Pallier can also do), you've got FHE; that is, you can compute any combinatorial function of encrypted (binary) inputs.

Here's how it works, you can construct the NAND function:

$NAND(x, y) = (Enc(1) - x)\  OR\  (Enc(1) - y)$

If we limit $x$ and $y$ to being either encrypted 0, or encrypted 1, then the result of this is an encrypted 1 unless $x$ and $y$ are both an encrypted 1; in that case, the result will be an encrypted 0.

The $NAND$ function is complete; that is, we can create any combinatorial circuit using enough of them.