For a start, TEFL and TESOL are two different entities so you'll need to be more specific with your query.
*TEFL - Teaching English as a Foreign Language.
Is a designated course but is also used in language as a noun. For example, "I could go to that college and get a tefl qualification.."
**TESOL - Teachers of English to Speakers of Other Languages.
It is an association and a field of profession, not a qualification. For further info please see
http://www.tesol.org/careers/counsel/whatistesol.html - it'll save me a page of writing.
As with any course, check prices, validation, type of qualification and accreditation of colleges providing them. They vary VASTLY from country to country and it's up to you to be in the know.
Secondly, Italian schools do employ non-EU citizens. You just have to get off your arse and, once providing their stated requirements, apply for the position offered.
Thirdly, obtaining a job is as easy or as hard as you make it. If teaching English in Italy is something you really want to do then no amount of hearsay from your information sources is going to put you off. Learn Italian, contact an Italian school, research requirements, factor your needs around theirs....it kinda carries on from there, you know?
Overall, get up, get out there, get your own information (the Italian Consulate is an excellent source of relevant info...they even have an Education Section! Wow!) and then make your choices accordingly.
Contrary to claims made in here about Italian teachers (a lot of whom are multi-lingual in addition to being fluent in English, by the way) being 'crap at English teaching' and having their children 'subjected to poor teaching methods' (aside from the fact that, technically and socially speaking, American English is a derivative of the English language and are not necessarily the same thing), Italian schools do take care in who they employ, how they employ them and what they are employed for. It's up to us, the foreigners, to step up to the plate and give them what they require and to the international standard that is demanded. And to teach English to an international standard you must be proficient in the English language, period

A lot of people mistakenly think that being a native speaker of English gives them automatic expertise. Um...that ain't necessarily so

And, before I get lambasted about the American dialect, I would point out that the same occurs, for example, with Spanish too. Latin American Spanish is not acceptable in schools even though it is often seen to be for all intents and purposes in America, "Spanish". Internationally, it's not.

As for that elusive job, if that ship isn't coming in, you get in the water and swim out to it.
