Known as Britain's finest infantry regiment, the 23rd fought in more actions during the war than any other single-battalion regiment.
And, yes, the spelling is both incorrect and accurate.  The majority of the troops were English, not Welsh.  The Regiment was named as it was because it was raised by the Prince of Wales, who also was not Welsh.

See their museum, mostly in English, here:  http://www.rwfmuseum.org.uk/index.html

Or just want to read about them:  http://www.regiments.org/regiments/uk/inf/023RWF.htm

If you want to join, in English or Welsh, see:  http://www.rwfnet.co.uk/

If you want to join the version with kinder Sergeants, see:  http://www.geocities.com/the23rdfoot/