Before shopping, try to actually shoot the various sights at close/mid/long-range. I used to prefer the Buffington sights, especially for long range. As my eyes have aged, I've found I can shoot the 1879 sights about as well as I could the Buffingtons when I was younger.
Trapdoors are a wonderful thing for shooters! They were the end product of 200 years of evolution of muzzleloading muskets and rifled muskets. The lock is a thing of beauty, designed to soldier on through accidents, neglect, and battle damage. The sights were intended to be functional for a pooorly-trained soldier while still allowing a well-trained soldier to use them for individual targets or volley fire on an are target.
Of the 20-30 trapdoors I've owned over the years, I've only seen a limited number of broken parts. Missing parts are more common. Fortunately, they made about a gajilliion trapdoors, so parts (at least for the 45-70s) are easily available. The trapdoor is also fairly easy to work on, so almost anything is fixable.
Before anything else, I check the bore condition. I know I'll be shooting BP and cast bullets in the rifle, so I have little tolerance for a rough bore. The problem is that the bore will often be crudded up with layers of fouling, to the point that sometimes the rifling isn't visible. In general, if I can see deep pits, I reject the gun. If the muzzle is battered or out of round, I reject the gun--cleaning with that abominable metal rod can result in muzzle damage, and I don't like having to counter-bore a shooter.
I check the chamber for damage. Damage is usually limited to corrosion, or scratches due to some idiot prying out a broken case with a screwdriver/ice pick/etc. Once in a while you'll actually find a gun sold as a wallhanger just because there is a broken case in the chamber; this can usually be removed with the proper tools.
Inspect the sights for damage. If the front sight is interchangable, damage to the blade is less of a concern. The problems I've seen here are bases broken loose from the barrel, slots for the blade cut over-size to fit a thicker front sight, and corrosion. Rear sights, make sure all the adjustments work smoothly--you may need to oil the sight before you can test this. Rear sights can be re- built or re-placed, but some (Buffingtons for carbines, for example) are hard to find and expensive. You'll have to use your best judgement here. If the sight is a mass of rust, plan on replacing (and use this as a bargaining point).
The action is fairly simple. Arizona Trooper and Drydock covered the main issues with teh breechblock. Check to make sure the extractor hook that catches the cartridge rim is present, and sharp. Check the firing pin to make sure no one has removed the tip so the rifle won't fire, and that the pin moves freely. On the lock, make sure the tumbler has 3 notches (unless it is an early model, or one of the Bannerman guns fitted with an earlier lock: then you should have a solid half-cock notch and the usual full-cock notch). Make sure the hammer will not fall from the first two notches when the trigger is pulled.
On full-cock, make sure the hammer doesn't move backwards slightly when the trigger is pulled, and that when at full-cock you can't push on the back of the hammer and make it fall. Either would indicate problems with the tumbler or sear, and should be corrected before shooting.
Trigger pull is going to be heavy and long. Yeah, there are ways to work on this. I've had trapdoors I re-worked to a 3 1/2-4# trigger pull, and others that I fitted with set triggers. . . but either alteration is not allowed in some competition, and can be expensive custom work if you can't do it yourself.
Check for cracks/previous repairs in the wrist, usually coming from the lock bolts (due to over-tightening) or through the wrist (due to being dropped). You can also find cracks/previous repairs behind the lock, due to the lock being hit when the rifle was dropped. Personally, I think most such damage was due to rifles falling when stood in a corner on a slick floor. . . .
Pitspitr mentioned bent barrels. I've had this come up on a couple of rifles too. Since you can't look through the bore, it can be hard to detect until you shoot the rifle.
If I were coming in as a novice looking for a shooter, I'd look for a rifle someone was already shooting so I could test-fire it. One thing about trapdoors being so common is that many shooters do some trading this way. (Lord knows I'm always searching for the perfect rifle!) You'll probably pay a bit more this way. Second-best would be to take someone familiar with the rifle with you when you shop.