Your scope mount sounds like a Weaver type base. Nothing wrong with that mount at all on a low recoil 357MAG, they will handle far more than that cartridge. And there is nothing wrong with the base being mounted in the rear sight holes on the barrel... that is typical of most scope bases on all TC barrels. If the base screws are not too long and the base is tight to the barrel it is just fine. Rings should be lapped for maximum contact with the scope tube to be done right... and the right screws snug. Even so i doubt the scope is moving. TC scopes are well made, so doubt it has any problems either.
Your accuracy problem is most likely shooter technique, how supported, possibly the load or the trigger. Contenders are capable of having excellent triggers - if yours is not it might be part of the problem. The load is easy to fix by working up hand loads to find what the barrel likes best in bullet, powder, primer, seat and crimp. But most barrels will also shoot factory ammo pretty well. Not as well as a handload worked up for the barrel though. As spinafish said, off a rest support the forend just in front of the trigger guard ONLY, and do not rest the grip on the bench (vertical stringing). Use your off hand to support the grip and to adjust for elevation. Keep in mind that there is a big difference between shooting a rifle and a handgun... the pratice needed to shoot any handgun well is many times more than for a rifle. You also need to realize that shooting a Contender well takes lots of practice and learning the technique for the slow lock time it has. They are very easy to wander off target with from squeeze to fire. But they are very capable of exceptional accuracy in the right hands though, and 8" of barrel is plenty for 50 meters with groups 1/3 of or even more than what you are shooting off a rest so far. Having had a truck load of Contender handguns and hundreds of both factory and custom barrels since soon after they first came out, I can say that I had very few that were not very capable at 100 yards or more, many that were very capable at 500 yards, a couple to 1000 yards, and most gave up very little or nothing at all to rifles.
FWIW