All kinds of changes have been happening at the Mexican immigration department on policy and in technology for applying for and obtaining a work visa which was formally known as the FM3 - it is now simply called No Immigrante, and with fewer categories to apply under. Those which affect most foreign TEFLers in Mexico are Independent status, employer-sponsored status, and rentista which is what most retired snowbirds have.
All in all there have been few changes. Instead of a passport sized booklet, the visa in now a photo ID card. Some of the application process has been moved online and it generally takes a little less time now to process the visa.
There's a discussion about the new process over at Dave's ESL Cafe.
I'm newly-arrived in the DF and in the process of applying cold turkey at a number of schools. In an interview yesterday, I was told that the process has changed so that you don't need a sponsor and there is one visa/permit for everyone not applying for permanent residence. I haven't found anything on the forum or the internet about this, so I thought I'd ask here, as it looks like a lot of people are going through the application process right now.
As I understand it, the old book has been replaced with a card, but that is the only change I've found so far.
PS If you know of any good job openings in the DF, be sure to let me know!
I'm going into migra on Tuesday to renew my visa and to help someone get their first independent visa (no sponsor as you note). I'll post the most recent checklist here for new visas. At last check, the paperwork for the card is not much different from that for the old booklet.
There are apparently going to be more changes coming later this year though.
and I continue with:
For the moment, nothing has changed regarding the independent visa. You still need to pay for the visa at the bank using a form they give, and bring in the receipt, original and copies of your passport, original and copy of the application printed from the migra website, copy and original of your degree and/or teaching qualifications, and a letter in Spanish outlining what you intend to do independently and how you are qualified to do it. File that and they summon you back to complete the process bringing in photos and another short application, proof of address, take your fingerprints and it's done.
I asked some staff at DF migra about the upcoming changes but they had very little concrete to say. They did confirm that the rumour of no longer being able to turn tourist or business visas into work visas from within Mexico is not true.
The discussion continues, adding detail on bank deposits, taxes, and apostilles for foreign documents. More at the link above.