Occasionally someone will take a Krag to one of those antique military rifle shootoffs and
@Slamfire might know something about that. There was a weird speedfeeder that is a serious collectible made that you might be able to duplicate for it.
On the mag, a common problem is a bent hingepin which makes it difficult to open and close the mag along with a small metal rounded triangle which is pinned into the bottom of the receiver. If this is messed up, it can lead to misfeeding issues. Some will feed spire points from the mag and some won't as the issued round was a round nosed bullet. Do not plan on hogging out the receiver feed ramp as it is case hardened and you will get a short life. The Krag is a rimmed cartridge which is good because the Krag is not really setup for gas events outside of the chamber. You do have to load the Krag in a certain way to avoid rimlock because it is a rimmed cartridge.
The bolt is a PITA to remove and requires a third hand to get good at it. Commonly, extractors can get damaged and need replacement and the extractor assembly is RIVETED together. and the bolt itself it a one lug design which is enough for the cartridge that it is chambered for. Some idiots would lap the bolt lugs or the receiver lug recess so that the bolt handled would bear and then fire hot rounds in it. This is idiotic because they lapped through the case hardening and the firearm is now not very safe. If the bolt handle bears at the back on the receiver, don't buy as it is ruined.
The military went through trying to "improve" the issued Krag rounds and ended up having to backtrack after a bunch of them cracked the lugs on their bolts. The Army had to have replacement bolts made to makeup for this disaster. That is one of the reasons that you can still get NOS bolts for it because these rifles were called back into service for rear echelon troops during WWI due to severe shortages of new rifles for front line troops. For that reason, watch out for a cracked bolt lug and more uncommonly receiver damage from rebarrelling. The Krag is difficult to rebarrel without a special receiver head that engages the bottom recesses of the unusual receiver. Occasionally Bubba can create some damage here if they were heavy handed in rebarrelling--those with Springfield 1903 barrels are the usual suspects and this damage to the bottom of the receiver can be hidden if inside a stock.
I already mentioned the trigger but a few misguided souls tried to make the trigger single stage instead of the two stage and you would need to replace such a trigger/sear which is not that difficult. There were a few headless cocking piece Krags made for a bit faster lock time so avoid these. Otherwise than removing the extractor, the bolt itself is relatively easy to break down. Watch out for damaged firing pin tips (these are like the 1903 with a rod and replaceable firing pin tip) that is deformed or a cocking rod that is damaged. Especially scrutinize the parts of a rifle bolt that have demonstrates extensive pitting around the firing pin hole as it is probably piercing primers now and again.
Normal stuff like headspace (.303 gages work for this and get the coin kind), barrel and chamber conditions are just as any other except watch out for wildcats. Bore diameters tend to wander both from wear and when manufactured. What is not normal about the Krag is that the front sight base is brazed on and uses an incredibly small pin to retain the sight blade. The sight base can crack under use and the sight blades can be damaged rather easily. The ones using 1903 barrels have 1903 front sights which are better frankly than the Krag's. Sporters often have a variety of commercial front sights and the 1903 front sight was often added. The issued rear sights are attached with some incredibly tiny screws and these were often buggered up or broken off during rear right removal. This usually requires making a larger holes for the sight to attach and using a modern threaded screw as Criterion did in their new barrels. Scoping these normally requires either using a scout scope mounted forward or a side mount scope. Have no idea about sight bases available for these.
Did I mention that the stocks were fragile? Well, proper fitting is absolutely required for a Krag stock as it is barely a one piece stock. The floor of the receiver is supported by incredibly thin wood and the wrist of these often gets cracks as well as the tang area. Improper fitting leads to chipping and cracking and as the wood is over one century old, people have globbed all kinds of finishes on them and sanded them down to slim them for sporting purposes. GunnyUSMC has probably worked on a Krag stock and I did twice--one to extend an existing cut stock at the front band and the second was to try to restore a stock broken in shipment which was less than successful due to the thinness of the wood. A few places used to make repro stocks but those currently are few and far between. Macon Gunstocks is one that I have seen still making them and they pop up on auction sites now and again. Cut stocks are fairly available.
The second shock is that handguards for these are astronomical and because each of the different sight types requires its own special handguard--you often have to go with repros and inlet them yourself.
examples of the different handguards
https://www.bing.com/images/search?view=detailV2&ccid=OvO6nQbq&id=51046C48955EA0565AFD317A51ED07791E713E2B&thid=OIP.OvO6nQbqCSDqF82rOP5-BAHaEt&mediaurl=http://www.kragcollectorsassociation.org/kca/Photos/handguards.jpg&exph=458&expw=721&q=krag+handguards&simid=608015678707206107&selectedIndex=5&qpvt=krag+handguards
One reason that these are so scarce is that they are thin and use riveted prongs on the underside to secure the handguard to the barrel (similar to the SMLE rear handguard and about as fragile.) People trying to remove these without gently popping them loose with the sight blade raised and then navigating the handguard to perpendicular to the sight crack or break them upon removal.
Last, the 1901 and 1902 sights are imho the best for accurate work with the 1901 being a slight favorite. The 1901 was the basis for the WWI era Springfield sight and it duplicates the older Springfield Trapdoor Buffington sights (because the General that approved them for Ordnance was the same guy) and it is adjustable for windage and has an incredibly tiny peep sight for distance. The Crozier 1902 sight is basically an 1898 open sight like the SMLE used but with a tiny peep sight mounted to the rear of the sight on a foldable leaf.