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There is a travel site called TripAdvisor that claims to recognise
false reviews. I've heard of members trying to post positive reviews
about their own motels and getting busted. Even though they don't have
a static IP address, how would the forum admins recognise the same
posters?

Someone in the industry suggested that it might be to do with the
computer's mac address. How do forum administrators actually see this
information to block users?

There is a product called Hide My Mac Address. How do you know if the
programme is hiding the crucial information? You can do a "whatismyIP"
but apart from looking in your ipconfig, how do you see what mac
address you are broadcasting?