any of his employer, bank, referee or any other source

The sentence is a bit awkward, and not correct grammatically, although the intention of the writer/s is clear.

It may be clarified by additional punctuation, thus:

-The Customer further authorizes the Bank to contact any of: his employer, bank, referee or any other source.

-The Customer further authorizes the Bank to contact his employer, bank, referee or any other source.

Thank you McTag.

What's Punkey's first language? UK or US English?

I don't know, but his solution was more elegant than mine.