The words are ambiguous. The notation is not.

Wiki is not the most reliable source, however, it does give good links usually - and that's true in this case. Their reference is Dr. Math and I find him usually dependable.

Wolfram gives a result I expect:
http://www.wolframalpha.com/input/?i=10+meters+squared

However, unlike you I

1) can admit that I might possibly be wrong, and
2) am not afraid to consult someone who knows more than I do,

so I will send an email to Dr. Weisstein at Mathworld to ask for clarification.

If there is an inconsistency here, it's only in the words which are ambiguous and not in the notation.

---
Here's the message I just sent to Mathworld.

Inconsistency.

According to http://mathforum.org/dr.math/
10 meter squared <> 10 square meters

However, Wolfram Alpha provides a different result:
http://www.wolframalpha.com/input/?i=10+meters+squared

Could this be the result of an inconsistency between British and American usage?

It seems clear that using standard notation eliminates the inconsistency: 2m * 2m = 4m^2 (regardless of whether one calls it four meters squared or 4 square meters)