Okay, first of all, there's a lot of misinformation being thrown around in this thread.
Century Arms is an importer, and they also manufacture firearms (usually converting a select-fire rifle such as a FAL, CETME or AK-47 variant into a semi-auto, from parts kits) which have a well-earned reputation for off-and-on quality.
However, the milsurp bolt-actions they are importing are not parts-jobs, unless they were parted together at the remanufacturing plant in their home country half a century ago before being slathered with preservative and packed in warehouses. The quality-control issues are more to do with the original condition of the firearm itself after being used or poorly rearsenaled, and Century has nothing (thankfully) to do with that besides grading the items they import.
Buying from Big-5 is literally a crapshoot if you aren't knowledgable enough to know what to look for in a milsurp item, but that goes for gunshows and online auctions as well. Don't buy a used gun that you can't inspect first, is a good rule to live by. Bring a cleaning kit and be prepared to use it when you go to look at milsurps with money in your pocket.
Sticky-bolt syndrome is a common problem, and has a simple, if intensive, solution. For what it's worth, I've not had this issue, as I use a foaming bore cleaner and this will remove anything sticking in the pits of the chamber.
Anyway, to innacurate shooting.
First of all, as Cosmoline mentioned, the two screws holding the action and magazine assembly in the stock MUST be hand-tight. Don't torque them, just use a screwdriver and wind them in there as hard as you can. Make sure the action fits into the wood properly, and that the stock is not warped.
Change ammunition type. This can't be emphasized enough. I have yet to encounter a rifle that is not finicky.
None of my mosins will fire Brown Bear accurately, for example, nor will they throw Czech training ammo in anything resembling a group.
However, as I have tried nearly a dozen brands and surplus ammo types, I have discovered that they all like the Wolf black-box softpoint, and FMJ.
I would not count on that being consistent with any additional rifles I acquire, but would test every cartridge again just to make sure.
Best ammo I've found:
Wolf black box SP and FMJ
S&B softpoint
Hungarian yellowtip heavy ball (from my M39)
Polish light ball (from M39 and father's M91/30)
Czech silver-tip light ball (from M44)
As far as my own experience with Mosin rifles:
Hungarian M44- sewer bore, but a nice action and trigger. Pretty much shoots like crap, but acceptably well for woods hunting (5 moa) with Wolf SP. I'll be bedding the action into its hacked-up ATI stock, and doing a trigger job, to cut that down a bit.
Finn M39- simply a gem. It shoots Wolf SP into 3" groups at 200 yards with open sights. Beautiful rifle, handles and shoots well. I need more of these.
Remington M91- my collection's crown jewel. I bought it for $100 at an ACE Hardware, willing to accept its sporterised condition for an off-chance at an excellent rifle. A scout-mount from makarov.com was just the ticket, as the original rear sight assembly had been removed and a rudimentary peep sight literally screwed onto the back of the bolt. Even with a cheap little BSA 2x scope I wrung a couple MOA groups out of the rifle with some S&B and Wolf softpoint. I'm moving up to a 4x Simmons, and expect to see great things from this rifle built in 1917 for the Czar's army.
Edit to crow a bit:
That M39 Mosin tied me for first place in last month's High-power match at the local range. It was a small crowd, but I was shooting against customized rifles and handloads with a 60+ year old military rifle firing surplus Hungarian heavy-ball. I would demurr that the weekly shooting schedule I work at is part of that victory, as well as luck, but still; I would not have placed if the rifle itself was not an excellent performer.
Century Arms is an importer, and they also manufacture firearms (usually converting a select-fire rifle such as a FAL, CETME or AK-47 variant into a semi-auto, from parts kits) which have a well-earned reputation for off-and-on quality.
However, the milsurp bolt-actions they are importing are not parts-jobs, unless they were parted together at the remanufacturing plant in their home country half a century ago before being slathered with preservative and packed in warehouses. The quality-control issues are more to do with the original condition of the firearm itself after being used or poorly rearsenaled, and Century has nothing (thankfully) to do with that besides grading the items they import.
Buying from Big-5 is literally a crapshoot if you aren't knowledgable enough to know what to look for in a milsurp item, but that goes for gunshows and online auctions as well. Don't buy a used gun that you can't inspect first, is a good rule to live by. Bring a cleaning kit and be prepared to use it when you go to look at milsurps with money in your pocket.
Sticky-bolt syndrome is a common problem, and has a simple, if intensive, solution. For what it's worth, I've not had this issue, as I use a foaming bore cleaner and this will remove anything sticking in the pits of the chamber.
Anyway, to innacurate shooting.
First of all, as Cosmoline mentioned, the two screws holding the action and magazine assembly in the stock MUST be hand-tight. Don't torque them, just use a screwdriver and wind them in there as hard as you can. Make sure the action fits into the wood properly, and that the stock is not warped.
Change ammunition type. This can't be emphasized enough. I have yet to encounter a rifle that is not finicky.
None of my mosins will fire Brown Bear accurately, for example, nor will they throw Czech training ammo in anything resembling a group.
However, as I have tried nearly a dozen brands and surplus ammo types, I have discovered that they all like the Wolf black-box softpoint, and FMJ.
I would not count on that being consistent with any additional rifles I acquire, but would test every cartridge again just to make sure.
Best ammo I've found:
Wolf black box SP and FMJ
S&B softpoint
Hungarian yellowtip heavy ball (from my M39)
Polish light ball (from M39 and father's M91/30)
Czech silver-tip light ball (from M44)
As far as my own experience with Mosin rifles:
Hungarian M44- sewer bore, but a nice action and trigger. Pretty much shoots like crap, but acceptably well for woods hunting (5 moa) with Wolf SP. I'll be bedding the action into its hacked-up ATI stock, and doing a trigger job, to cut that down a bit.
Finn M39- simply a gem. It shoots Wolf SP into 3" groups at 200 yards with open sights. Beautiful rifle, handles and shoots well. I need more of these.
Remington M91- my collection's crown jewel. I bought it for $100 at an ACE Hardware, willing to accept its sporterised condition for an off-chance at an excellent rifle. A scout-mount from makarov.com was just the ticket, as the original rear sight assembly had been removed and a rudimentary peep sight literally screwed onto the back of the bolt. Even with a cheap little BSA 2x scope I wrung a couple MOA groups out of the rifle with some S&B and Wolf softpoint. I'm moving up to a 4x Simmons, and expect to see great things from this rifle built in 1917 for the Czar's army.
Edit to crow a bit:
That M39 Mosin tied me for first place in last month's High-power match at the local range. It was a small crowd, but I was shooting against customized rifles and handloads with a 60+ year old military rifle firing surplus Hungarian heavy-ball. I would demurr that the weekly shooting schedule I work at is part of that victory, as well as luck, but still; I would not have placed if the rifle itself was not an excellent performer.
What makes it even more ridiculous is when I have owned dozens of milsurp rifles and regularly compete in monthly milsurp rifle matches and see hundreds of milsurp rifles fired in competition 
