While you pour ridicule over my former haircut, I will somber-mindedly address the questions here:
"can anybody tell me the advantage and the disadvantage of having a zero fret?"
A question of religious belief. The open string is then to sound more like a fretted note, but I love the sound of an open string and that it differs from a fretted note. With the exception of the low E, you can play all open string tones fretted on a bass anyway. Duh!
A probably more sensible advantage is that the issues of the nut not being notched deep enough for comfortable action or too deep for then too much string buzz do not apply with a zero fret. Size of string notches is irrelevant as the string is guided over the zero fret for the first note in any case.
Uwe
