First thing I did was swap out the pickguard. I'm no fan of tort at the best of times, but modern Fender tort isn't particularly great and I really don't think tort ever suits a greenish guitar. After much deliberation, I went for a Fender Pure Vintage guard in eggshell from an eBay seller in the US, which worked out cheaper than buying one here in the UK. These guards are expensive, but the bevel is more-or-less vintage correct, and the eggshell is a really nice subtle parchment-ish colour, not a stark white. It looks in keeping with an original '65 or '66 Jazzmaster.
The guitar is lovely. Under 8lbs and very loud acoustically compared to my other guitars. Everything works well, even the vintage-style bridge (which I'll keep on the guitar, I see no reason to change it, although I have put a bit of loc-tite on the grub screws).
The pickups sound great to me and can cover the whole spectrum, from warm and dark to thin and trebly. Switching between the pickups, and utilising the tone and volume controls, you can create a lot of sounds. The rhythm circuit is very usable too - actually only subtly darker than the neck pickup on the main circuit.
The fretboard is nice and dark, although with a subtle lightness on one side, which gives it some lovely character. I'm really enjoying the 9.5" radius and vintage tall frets - much easier to play than a 52 reissue Tele I had a while back. The neck has a nice taper, thickening up significantly towards the 12th fret. Pearloid dots and binding at an extra touch of class, and I actually prefer the non-matching headstock on this guitar - I think with the binding it would look a bit too bling for my tastes.
The finish has that hard-to-describe quality to it that nitro often has. It just looks 'classier' and more expensive than a poly finish. It's quite thin and pretty easily scratched/dented. I've added a photo below to show the first chip I've put in it, and I've no idea how or when this happened. I wonder if this finish will check at some point? One thing that's a bit disappointing on these modern nitro Fenders (and I think it's the same on the AV65s and the Marr Jaguars) is that they don't seem to have a white primer or base-coat under the metallics, so when they wear or chip they don't look quite the same as a real vintage Fender.
Don't worry about the chip, it makes it more human and unique. Poly can be too indestructible, although I agree this aging is not the same as the vintage Fenders.