I don't think it's grammatically incorrect, although it does sound awkward to many people, including me. One may say, for instance, "Yesterday has past, and today is the following day." Here is an implied, "The last customer" as in, "The last customer has gone, and now I may help the following customer." It sounds wrong because it sounds to many of us like the speaker is attempting sophistication unnecessarily.
I also think it's a NYC quirk, similar to the use of "on line" vs. "in line", as in, "We are standing on line waiting for the cashier." If you really want a full dose of NYC cashier regionalism, wait until you hear, "I can help the following customer on line." Not wrong, but very specifically NYC, and wide-spread.
Fundamentally, I think this is more of a class thing and than a grammar thing (IMHO). FYI, "on line" comes from the NYC public schools, where kids had to literally stand on a painted line. It bugs me a bit, but I'm choosing to get over it. I've not heard either of these used outside of NY. Curious to know if it happens elsewhere.