Two problems related to engine clicking and tapping noises have been reported for the 2007 BMW 328. The most recently reported issues are listed below.
Car has horrible lifter ticking noise. Started around 58k miles, now up to 61k. BMW knows about this issue and have even went as far as issuing a new (revision in 2009) service bulletin and redesigning the head and lifters. They don't want to issue a recall notice for their own design flaw because of the cost associated with replacing these parts. I change the oil every 3k miles and have been noticing ferrous metal flakes in the filter caused by the lifters being starved of oil due to the oil ports in the head being too small to allow adequate oil flow to them. One would expect a BMW to last a little bit longer than 60k miles before any issues like this arise.
2006, 2007, and 2008 BMW 3 series have a metallic ticking noise from under the engine.