Pronounciation
With its roots in an ancient culture and its misleading spelling, "Cait Sith" is probably the most commonly mispronounced name of all of the names of characters in Final Fantasy VII.
Cait Sith is not actually pronounced "cate sith", as indicated by how it's written; rather, it is pronounced "ket shee", as provided by the Japanese version: 
(ketto•shii).
For the most part, this coincides with the original pronounciation of the name of the cat from the Celtic myth that Cait Sith was based upon. In the ancient Celtic tongue, "cait" is actually pronounced
"caught", rather than "ket" as the Japanese vocalisation suggests. "Sith" or "sidhe", however, is spoken as suggested.
The discrepancy between the original "cait" and the Japanese translation may be due to a number of factors. If it had been directly translated, "cait" would have read "katto", which is already a known word in Japanese: the word for "cut"! It is a little bit odd, which is perhaps why the alternate pronounciation was chosen. Furthermore, the myth of Cait Sith originates in a number of different countries in the Celtic collective, and different dialects may have given way to alternate pronounciations—"ketto" Sith may have been one of them.
Mispronounciation
During a conversation with Cid Highwind in Dirge of Cerberus, Cid begins to say Cait Sith's name but cuts himself off after "Cait", as he meant to say "Reeve" instead. What's notable about this scene is that Cid pronounces "Cait" as "cate", which is incorrect, so far as the original pronounciation is concerned. One could argue that the Japanese pronounciation allows for this, as the "e" sound in "ketto" could be the Japanese equivalent of an English "e" with either a "ey" or "eh" sound. Then again, Cid does have a fairly thick accent, which could also account for the mispronounciation.
Origins
Those versed with Celtic legends may recognise the name "Cait Sith", and perhaps even Cait Sith's design, undoubtedly based upon descriptions of the mythological cat of the same name. Two myths of Irish Gaelic and Scottish origin stand out in particular.
One record of the name of Cait Sith originates from early Irish Gaelic mythology. Cait Sith literally translates into "Fae Cat", and was the name of a legendary feline figure. This faerie cat reigned as the king of all cats and was a symbol of luck, much like our own Cait Sith (except thought to be perhaps a bit more reliable in that regard...).
Cait Sith, or Cat Sidhe, can also be found in Scottish legends. Stories refer to a black cat as big as a dog with a patch of white fur on his chest -- this describes Cait Sith's appearance perfectly. This faerie cat of the Scottish legends was thought to be a witch in disguise who haunted the Scottish Highlands. Cait Sith, recognising his namesake of myth, flaunts a Scottish accent.
