The five-speed gearbox was a genuine advance for the Giulia over its predecessors, and it is a strong, pleasant unit — with one well-known weak point to check.
A strong box with a known weak spot
The Alfa five-speed is robust and satisfying to use, but second-gear synchro wear is its classic weakness. As the synchromesh tires, second becomes obstructive — especially on a quick or cold change.
What to feel for
On a test drive, make some deliberate, brisk changes into second, both up and down, cold as well as warm. A crunch or baulk going into second is the tell. A little reluctance when stone cold that clears as the oil warms is common; a persistent crunch is worn synchro. While you are there, check the clutch action, listen for bearing whine, and see that the box doesn't jump out of gear on the overrun.
What it means
A worn second-gear synchro is not a disaster — these boxes are rebuildable and parts are available — but a rebuild is money, so it belongs in your negotiation rather than as a surprise later.
The good news
Kept topped up with the right oil and not rushed when cold, these gearboxes last well. Second-gear synchro aside, a healthy five-speed is one of the real pleasures of the car.