I've had cab fares take a month or more to appear on my Amex statement but usually they are there in a few days at most. Apparently a lot of cabbies prefer to use the manual system because at the end of their shift they can take the receipts to the depot and get cashed out on the spot, doing it electronically it apparently takes them a month or more to get paid!
I too have had a dodgy experience with a manual transaction, the cost was supposed to be around $14, the transaction came through as being $124 or something like that, the idiot probably thought the company's paying he won't even check, but oh how wrong he was!
As a result I refuse to pay using a manual machine and if there's no other option I will take a photo of the Driver's ID card and give him a quick rundown of my past experience with a manual transaction, that way hopefully he won't try to pull any swifties!