My 530d got same problem as in this thread 530D Massive Turbo lag but then pulls great???, big delay before turbo comes in.
I have car just for few days only. Today I have found that exhaust manifold got a crack, and alot fumes comes out(looks almost like engine smoking). Its there possible reason for acceleration delay? I have watched videos tonight on youtube about how turbo works and exhaust is important to it. I have left car for mechanic today to take off manifold and weld a crack. What is your opinion about it?
(sorry for language)