There are 3 possible problems.
One would be with one of the 870 Special Field guns. They were only a handful made for a few years. They used a shorter 3 round mag tube and the barrel ring is located in a different place. Those barrels will not interchange.
Remington made some "Light Contour" barrels for the Wingmaster. Standard barrels used thicker steel in the barrels. They will all fit on the receivers, but a standard barrel on a gun meant for a "Light Contour" barrel might need some wood removed from the fore end to leave enough clearance to work the action. Might not, but it could be a little close.
Those are pretty rare.
The most common issue is that Remington used 2 different magazine caps to secure the barrels. Most older guns used a ball detent system. Newer guns use a different system. If swapping old and new systems you need to get a little creative to keep the barrels tight. A rubber gasket between the barrel ring and magazine cap works. It isn't a major problem to overcome, but does need to be addressed or things will work loose every few shots.
Other than that it is pretty simple.
