Welcome Barrie, and sorry to hear of your problems.
There are a few points which are worth making, not all of which will give you cheer.
The GT is based on the 147/156 chassis, and whilst build quality certainly improved over the build run, there are inherent weaknesses in the design that will bring the odd chassis rattle, or suspension squeak. With a hatch as big as the GT hatch there is bound to be some movement in the body. These you may have to learn to live with..but not whilst you have a warranty. There are some known fixes for squeaking hatches on the GT, if it happens to you.
The build quality of 159/brera/spider is undeniably better, but the odd badun still gets through. Alfa are not alone in this by a long shot
I'm disappointed to hear about issues that should have been picked up at the PDI, particularly as the PDI is carried out at a dedicated PDI centre, and not by the supplying dealer. Their system should be robust enough to pick up this sort of thing before it gets to you.
Just make a list, make sure you keep a copy, and politely make your feelings known to the dealer. They should be able to fix all the problems you seem to have very quickly.
That aside..its a great car, enjoy your first Alfa, I'm on my fifth and havn't regretted any of them. If I want a VW fix I drive one of our other cars (a Skoda