The two things that affect shooting long range with a .357 revolver the most are the trajectory resulting from a low velocity and low ballistic coefficient and most .357 loads going transonic at an intermediate range. When projectiles slow below supersonic velocities they can become unstable, pitch, yaw, tumble and generally lose the consistency of their point of impact.
Most .357 projectiles start out with supersonic muzzle velocities of 1200 fps or more (1126 fps is considered supersonic under 'standard conditions', altitude, barometric pressure, etc.) The relatively high velocity of .357 Magnum even from a handgun-length barrel allows for a reasonable trajectory out to ranges beyond 100 yards. Under practical conditions (not test barrels in a reloading manual), I've shot bullets out of my revolver that were at 1700fps through a chronograph. Even with a 25 yard zero, they only drop an inch at 100 yards. But by 200 yards, they've dropped 20 inches. 300 yards, 70 inches or almost 5 feet. Even if I zeroed it at 100 yards, the hold-over at 300 yards would be 5 feet, 6 inches. With more common real-world muzzle velocities of 1350 fps for heavier 158 grain bullets, the hold-over at 200 yards is about 3 feet. Because of these steep trajectories, .357 Magnum is not really practical on critical targets or game at 200 yards, not from a handgun anyway. 100 yards, however, is totally practical and even within MPBR for something like deer with a 25-yard zero. I have not shot game at that range, but I have placed bullets in the A zone of a silhouette at that range, again shooting prone or standing but rested (like off the hood of my truck). Because the trajectory at 100 yards is manageable, making hits is just a matter of a steady hold and trigger control (I always shoot double-action by the way).
Now let's look at going transonic. If we start at 1700 fps, most handgun bullets will go transonic before 200 yards. If we're shooting something that is going to have a good terminal effect at those long ranges like a 158 grain Hornady XTP at 1350 fps, it will go transonic around 100 yards. It is possible to avoid this by starting out subsonic. Doing so could keep the point of impact more consistent but will result in a steeper trajectory. For example, if we started out at 1000 fps, it will drop 30 inches at 150 yards with a 25 yard zero, but the point of impact could be kept very consistent. If we zeroed it at 100 yards, it could be very accurate there and the hold-over at 150 yards would only be 15 inches.
Shooting off-hand, standing with no support, I hit plates at 25 or 30 yards, and silhouettes out 40 and 50 yards. At these ranges, the gun and cartridge have no real limitations. Bullseye and steel silhouette shooters work in this range all the time and do much better than I can. My only purpose for shooting handguns is personal protection, so I focus on more speed within 1 to 15 yards. Surprisingly, I was introduced to shooting IDPA targets at 40, 50, 75, 100, and 200 yards at defensive handgun classes at two different schools. I have since practiced 40 and 50 yards. I'll practice 100 yards for novelty on rare occasions. I consider 200 yards mostly impractical. I did hit a target at that range once with a 1300 fps cartridge. It dropped in from about 3' over and was probably down to a little over 900 fps. The target was steel, but I wouldn't be surprised if it slapped it sideways.