I just observed two switches in the network with different VTP Operating Modes, one is Server the other Transparent. The VTP Domain Name is the same. Is there any issues keeping the VTP Operating Modes different?
There aren't any issues. The problem that you'll run into is that if you're truly running a VTP domain, any vlans that you create on the server won't be propagated to the transparent mode switch. Effectively, transparent mode disables vtp on that switch.