Using So Called "unusable" Sub Net Addresses

By mistake I moved a OpenVZ VPS and set it up on the Network Address of a subnet. In the control panel of my data center no distinction was made between this and the other usable addresses of the subnet. Still the same I am somehow accessing the new location all right. There is a weird mail queue on the new location that tries to send mail with local destination to the old server though and some weird effects in Linux that ping gives an old address while dig gives a new address, but they might not be related.

Can somebody explain in simple terms what could be the disadvantage of this use of the Network Address or the trouble it could cause. My control panel doesn't allow mass IP change in the DNS so it is a lot of work to change them again, not to talk about the DNS confusion it will bring.