Welcome to the forum.
I have a 2.0 JTDM 140 Sportiva (Diesel), remapped to 180BHP.
It sounds great (admittedly it also has a full stainless cat back exhaust and an induction kit)
It goes like the absolute clappers
It drives and handles really well (mine is lowered on Eibachs)
It's quite a bit more torquey than the petrols (including the QV)
I get 55mpg combined, and that's with the majority of my driving being a short commute to/from work. The best I've had was 86.9mpg on a trip back to Worcester from Milton Keynes!
It looks fantastic - much nicer than the equivalent A3, Golf, Focus etc in my opinion.
The rear wiring looms on the earlier models are prone to breaking. The top and bottom of the loom housing were directly in line with each other which caused the wires to bend excessively, and eventually break. I believe Alfa sorted this in or around 2013 by repositioning the placement of the looms themselves, so that the top and bottom of the loom housing was offset, and the wires didn't fold back over each other whenever the hatch was closed. Mine is a 2013 and has the later arrangement - I'll post a couple of pictures up so that you can see my G, and the loom arrangement so you know what to look for - the position of the blanking plate in my photo is where the old loom arrangement would have been.
The paint is pretty 'fragile'. But that's not specific to the Giulietta, just Alfas in general - expect to see more than a few stonechips on the bonnet and possibly some road rash around the arches.
In my experience (2 x Giuliettas and a 159), they seem to be quite fussy on wheel alignment and tend to chew through tyres if they're not aligned properly. Easy solution though - just have a 4 wheel alignment done when you get the car (or ask the garage to do one if you're buying from a dealer).
Apart from that, there is nothing to look out for other than what you'd normally look at with any other used car.
Oh, and you'll love it!!