if you're shooting surplus, that'll be your first problem. It isn't all that accurate at all.
Once you start using commercial or hand loads, could be the gun. It completely depends on the condition of the gun. Many of them have been through at least one war then refurbed, so they vary greatly. Best bet is to keep buying and selling them until you get one that shoots well, then work with that one. There was a thread on sniperizing a mosin recently that has most of the pertinent info in it. That guy on youtube is using a very nice rifle that has a fair bit of tweeking to it... he's probably mostly original, but has done a low bubba bedding job, maybe tweeked the trigger, and spent a long long time working up loads that are perfect for it.