A little more history...
Jim is quite correct on the trigger/safety problem.
A little more info on the Model 600 series, They were originally a "bargin" rifle, compared to the model 700, and are fine little guns in their own right. Originally they had 18.5" barrels with a very slender contour and a nylon vent rib, along with the nylon triggerguard/floorplate. Blind box magazine, "shark fin" front sight, and a dogleg bolt handle with flat bottom knob, which kept it very close to the stock. The dogleg put the bolt handle above the trigger finger, and at least for me, was very fast to operate.
Calibers available were .222 Rem, (later a very few were factory chambered in .223), 243 Win, 6mm Rem, .308 Win, and a few in .35 Rem. There have been rumors of a handful in .30-30, but I have never seen any, or any info to document that fact. The same rifle in 6.5mm Remington Mag and .350 Rem Mag was called the model 660. It also had a laminated stock and a recoil pad.
The guns went through a few small changes during their short production life, and some model 660s apparently were made in standard calibers. I have seen one model 600 with a deluxe stock (contrasting forend tip, pistol grip cap), but this was not usual. I have a .222 with the laminated stock, which is supposedly only found on the magnum guns. At one point in the production, the vent rib was dropped, and the barrel was increased to 20", with a heavier contour.
After Remington dropped the model 600 rifles from its main catalogue, they contined to be made for a few years as the Mohawk 600. The cocking piece on the bolt was changed to the one used on the model 700, and they had the heavier 20" barrels. .308 was probably the most common, but I have one in .243 Win. I do not know if any Mohawk rifles were made in the magnum calibers, but I don't think so.
The model 600 action is the same basic action used on the XP-100 pistols, and is the same basic design as the model 700 (short) action, with some slight differences. The ejection port is very small, and a loaded round will only pass through it at an angle. The magazine is a simple sheet metal box which is open at the rear, and must be carefully fitted to the bottom of the action when installing it into the stock. Unless care is taken, the sheet metal box will pop out slightly, and if not noticed (and corrected), you can bend the nylon floorplate when tightening the screws.
The early guns were very light, going about 5 1/2 pounds (without scope), and the later guns about a pound more, due to the slightly longer and much thicker barrel.
My first deer rifle was a Model 600 in .308, and I still have it. My Dad bought it from Sears for just under $100, brand new (around 1965, I think), and carried it a couple of years before passing it on to me. The little carbine was a big stick in the Adirondack deer woods, considering at the time, 8 of 10 rifles carried there were Winchester or Marlin .30-30s or .32s. The odd rifles were either Remington pumps or autos, or Savage 99s, generally.
Col. Cooper did use the model 600 as the basis for his first scout rifle designs, as even out of production, no other bolt action then available came closer to what he was looking to build.
Remington replaced the model 600 rifles in their line up with the model 788, a completely different kind of action (rear locking bolt), detatchable magazine. (I think it was cheaper to make than the model 600, but have no real proof)
I have always loved the model 600, and felt betrayed when Remington dropped them for good. On the other hand, not everyone felt the same way, a lot of people at the time felt they were quite ugly. You either loved them or hated them, there didn't seem to be any middle ground.
Anyway, they are pretty good game rifles, but not (usually) stellar performers from the bench. The light barrels heat up fast, and tend to walk shots as they heat, so 5 shot groups fired rapidly don't look too good. Shots fired from cold barrels do much better. My original .308 only shoots about a 2in group @ 100yds. But it puts everything into that same 2 inches! 150s, 165, and 180s all the same. This is not typical performance, but it works for me.
With good optics the little carbines are at no real disadvantage for longer range shooting either, keeping in mind the limits of their cartridges. I still have a love affair with th Model 600 series rifles, and buy them when I can find them (and afford it!). They cost quite a bit more today than they did back then, but then, everthing does.