Ford Mustang: Problems and Solutions
The first common problem
Some 2005-2007 Mustang GT vehicles equipped with the 8.8 inch limited slip axle may exhibit a moan/groan noise when making tight low speed turns. This may be more noticeable when the axle is at full operating temperature. The noise may also be confused as originating from the brakes or steering system.
This is a documented problem and the dealer should replace the limited slip clutch pack. Since your dealer seems to be unaware of this, maybe you should get to a dealer that knows what he/she is doing!
Second common problem
Early build 2005 Mustangs had a problem with premature fuel pump shut off. The tank was redesigned. The condition may be due to the fuel tank vapor venting system inside the fuel tank.
If you are having this problem with 2006 – 2007 Mustangs, Ford claims that it is the pump that is at fault. Ford believes that some pumps deliver fuel at too fast a rate. Ford suggests that you try a different pump. Ford reminds that any modifications or alterations to the vehicle are not covered by warranty and are not recommended.
This info is from the two TSBs that are related to the Fuel fill problem. However, the 2007 is suppose to be fine.