TRANS FAIL SAFE is in most cases, not a faulty transmission.
Speed sensors (at each wheel hub), have nothing to do with needing a new transmission. I would check them, and clean if necessary (you can do this yourself, if you are slightly mechanically inclined). The first place to look would be the fuse box - always check tALL the fuses first. If you carhas the stock BMW exposed wire fuses - my suggestion is to replace them anyway, regardless of condition, with the newer style enclosed lastic fuses. The wire has been know to have intermitant connectivity issues which the new ones don't.
The TFS is a safeguard program that the car does so you WON'T mess up the transmission. This can be caused by a number of things, such as (for example) a misfiring engine, a faulty fuel pump, faulty throttle body, clogged injectors, clogge fuel filter, and the list goes on. You need to have the car connected to a BMW MoDic or GT1 Diagnostic computer at the dealer. CARSOFT, PEAKE or any of the "other" non-BMW diagnostic stuff usually will not help you here. As for your mechanic: does he have a house payment he is trying to make? The majority of TFS causes can be recified rather inexpensively (not like buying a new transmission).
White 1993 850Ci - 251,187 miles
Black 1993 850Ci - 125,508 miles