Not too many people, at a bazaar in Kabul or a gun show in Kalamazoo are going to let you strip a rifle down to it's components. But there are some things you can check without going to that level, and without having to be knowledgeable enough about a particular type or series of firearms that you can spot dimensional problems with parts. Which we'll get into, eventually.
Here's a shot of the bolts from the three rifles I started this series with. The Charger-Loading Lee-Enfield is on top, the Khyber Lee-Enfield #1 is in the middle, and the Constabulary Carbine is on the bottom.
They all look pretty similar in dimensions. And they should all be interchangeable. But they aren't. The Khyber bolt will not close in the other two rifles, though it will go into the receiver. The side lug on the Khyber rifle's bolt is 1mm too long, even though the overall bolt length is okay, but that's a tough call to make with a Mk 1 Eyeball, and who carries that kind of data around in their head? The other two bolts won't even go into the receiver of the Khyber rifle - because the slot in the bridge (rear) of the receiver is too narrow. Which also means that the bolt head of the Khyber rifle is dimensioned incorrectly. By this time in rifle making, the Brits were very uniform in production standards across the Empire and parts were mostly interchangeable as appropriate, even between rifles made in different countries.
Again, all that's nice, but usually the rifle has to be on the bench to make those kinds of checks. So, what's a quick and dirty way to check?
Screw threads. Especially the quality of the screw threads. Again - I know, what vendor is going to let you take out your multi-tool and start backing out screws?
They don't have to - if they'll let you take out the bolt.

First thing is look at the proof marks on the bolt heads. Gotta love the Brits, and to a lesser extent, most european nations marking rules - very helpful in sorting out fakes. If you are going to get serious about collecting european weapons, you should invest in some of the books about markings that are available - and I would get the books, they're more useful at a show though I suppose to the higher-quality web phones might get you sufficient clarity of the graphics on the web pages that cover the topic.
On the lower bolt you see the "x" which is really crossed pennants, meaning the bolt passed proof, then there is a Sparkbrook inspection mark (correct for the era and rifle, as the rifle is a Birmingham Small Arms (BSA) built rifle. On the Khyber rifle, it does have a crossed pennant, but it's on the outside of the bolt, not a common location, and the markings on the edge of the bolt head don't match any known Commonwealth markings (including Indian or Pakistani) - REI and something I have no idea what it is. There's another sign - itself not definitive, thanks to the efforts of "Bubbas" the world over, but the bolt head, in the shiny area near the end, has the waffle pattern imprint of a vise - a not unusual feature of the workshop-built guns, when they're clamped in vises for filing and polishing.
So, lets back the bolt head out of the bolt - you don't have to remove it to see what you need to see, but it's useful if you can. They guys who make these guns don't use fancy machine tools and lathes. These are artisanal artifacts (and these guys are good - I think they have collectibility from that aspect alone - just don't pay premium prices for something that it isn't!) and it shows in places like screw threads.

Those are machine-shop quality threads on the bottom bolt head, which is the original. The threads on the upper bolt head, the Khyber Special, aren't nearly as neat, tidy, and uniform. Nor is the machining job on the firing pins - the upper firing pin was ground to shape, not turned and polished.
Again, this next test is a bit tough to do in the bazaar or at a gun show. But if you try to swap the bolt heads, they won't swap. The machined bolt head, with it's narrow, neater threads will go in pretty far, but not far enough - and, if you push-pull on it, there's a lot of windage - the bolt head will move noticeably while seated in the threads.

The Khyber bolt head in the BSA-made bolt (the lower bolt in the picture) won't screw in very far before it binds up. When you have the bolt heads in their respective bolts - the machine made bolt head will have little to no windage, the handmade one will wiggle even when screwed in. Which doesn't bode well for the service life of the bolt, either. Bolt heads should always spin in and out freely and completely.
So - the quick and dirty check is to take the bolt, look at the proof and inspection marks, and check the quality and fit of machined threads. It helps if you know your target weapons well enough to know when things should be machined and polished vice ground and what sort of marks to expect. The differences will be pretty obvious.
This works for Enfield-style rifles. Martinis have a different set of cues. But thread quality of screws, regardless of rifle, can be an indicator.
So, keep that in mind, Heartless, when you're browsing the bazaars for us both!
Bill's probably closer to the mark... so to speak.
As I mentioned in the earlier piece, another good test is the QUALITY of the proof marks, and especially the quality of receiver and maker's marks, etc. The original factory-produced articles have neat, crisp, even markings produced by single stamps, usually aided by machine presses.
The repross will almost universally have unevenely spaced, poorly stamped markings because the makers are using hand-held individual letter stamps and a mallet to impress them. Thus you get uneven depth and anglesm spacing and linear aspects.
Some repros are VERY good, but with a little practice, and an understanding of HOW the markings are applied on the genuine articles, you can get a pretty good feel for what's genuine and what isn't.
There's a whole 'nuther article to write sometime about fake bayonets, swords and such accessories and how to spot artificial patinas and induced aging.
respects,
I've owned and fired dozens of genuine LE's but never seen one with a receiver slot wide enough to take a rifle.