I purchased this project car in April 2008 with the thought of at least partly replicating an Abarth. I got it from a collection in SoCal. It has most of the body work already done. Parts of both of the floor pans have been replaced. It has relatively little rust left, which is quite rare for an old Fiat.
Before we get too far into what I've done with it, though, just a couple of engine specs for the uninitiated:
It has a 767cc/46.8 CI motor which produced 32bhp @ 4800 and 38 lb-ft @ 3000 when new. Bore is 62mm/2.44". Stroke is 63.5cm/2.5". According to the Nov 1961 Road & Track Road Test, top speed was 72 mph and it did the standing 1/4 mile in 24.3 sec at 54.3 mph. 0-60 took 32.0 sec.
The gentleman I bought it from said that he stripped the car of all trim and took it to a body shop where the work was done. He got it back partly done, never put it back together, and eventually decided to sell it. It arrived at my door as you see in the pics but with all the trim bits in postal boxes. It's 95% complete, but I won't be putting together any time soon. I have put on only what is necessary to drive.
I received it with the engine bay in the above condition. Not bad, but definately needing some attention. The first thing I did after the general inspection was to catch up on some of the deferred engine maintenence. I worked on the oiling system first: changed oil several times, replaced the oil filter cartridge, cleaned the centrigual oil filter, and replaced the o-ring, which was now solid and leaking. I also added a oil pressure sending unit and guage from an 850 spider, so I wouldn't just have the warning light. To my surprise, it has very good pressure.
Next up was the cooling system. I drained the coolant, removed all three hoses, removed the water pump and radiator. I had the radiator cleaned and tested, flushed the engine, replaced all hoses, and purchased the correct radiator cap.
Last of the major systems was the ingnition system. I thought it was safe to drive at this point, but it was running like garbage. So, I mounted the voltage regulator (which I think is broken) to the correct spot in the upper right, replaced the points, wires, and spark plugs. It ran 100x better with just the wire replacement, but still misses some. Valve sticking, I think.
Here is the engine bay as I left it in the fall of 2008. I painted the valve cover. I replaced the stock distributor with one from an 850, which I had swapped out the points in favor of a Crane Cams XR3000 optical ingition system. Also, the coil is new and mounted in close to the correct location.
Other work I've done is replaced the brake fluid and bled the brake system. I've also replaced the transmission fluid and greased the suspension.
Feb 20, 2009 update: I took the car down for the winter. I removed the tank, battery, doors, seats, engine, and transaxle. The beginning of this year my brother and I rolled the car over on its passenger side so that I could do some work underneath the car. I'm taking the underside down to metal with a stainless wire cup so that I can kill any rust, then prime and paint.
Here are a couple of pictures of the car on its side...




I've also disassembled the transaxle which is sitting in about a hundred pieces on various shelves in the garage. It leaked badly and needed some serious cleaning, inside and out. I have a new gasket set, but am waiting for new inner axle boots, seals, and mounts. When cleaned and assembled, I'm going to run Amsoil 10W-40 Motorcycle Oil in it. I've heard it works very well in these.
After the car is ready to roll back over, I'm putting in the 903cc motor out of my 850 Spider (the motor with the turbo on it on page 3). I'm rebuilding it now, including changing the rotation of the motor since the 600s and 850s rotated in opposite directions.
Here are a couple of pictures the parts sitting on the shelves.
In this picture you can see my collection of severed heads... and carbs. Four heads (one from a Autobianchi), four carbs, two cams, two cranks, Abarth headers and exhaust. In the pink bags are the CBR throttle bodies and another engine block. That's the block I'll build to put the turbo on. There are also some USPS boxes on the top shelf that all the trim pieces came in.
These shelves have all sorts of parts in various states of progress. The most obvious of which is the tranmission housing. Also here is the generator, pistons, a brake caliper and hangers, and cog belts!

I think I'm on track to have it back on the road June/July.
More to come.
May 23, 2009 update: I've been busy. I removed the rear control arms, breaks, and hubs. I had the control arms and break plates sand blasted then I painted them with POR-15. They look nice, don't they?

I disassembled the transmission, cleaned, then reassembled it along with an LSD I got from Scuderia Topolino.

I'm in the process of cleaning and repacking the rear wheel bearings before I install them back on the car.

Also, I have the engine primed and ready to paint this weekend.

Sep 10, 2009 update: Work is progressing, but slowly. I've been ill this summer and it's now clear that the car won't be on the road this year. However, here are some pics of the work I've done.
The block is now Fiat factory green. I'm not sure the the name of it is though...

I finished grinding down the center and rear sections to metal. I glassed up a coupe of dime-sized holes in the rear, painted everything with at least two coats of POR-15, the coated the rear with rubberized undercoating. I had originally planned to leave the front section for next summer, but since I won't be driving it anytime soon, I thought I would continue that work this fall.
You've already seen the rear control arms, and in fact, the rear suspension is ready to be put back in place with the exception of two caliper brake plates. These plates will allow me to use Fiat 124 rear discs. They should be down by the end of the month.