Bill,
Sounds very interesting!
Like 500 Nitro said you must check which loading this rifle was built for as there were two different bullet weights used.
The 400-350 was loaded with the 310 gn bullet but there are a lot of Rigby doubles, often on Webley actions, which were built and regulated for a lighter 225 grain bullet.
This 225 grain loading was called the 350 No2 and is also a very good cartridge.
The true original velocity for the 350 No2 is often claimed to be the same as the rimless "350 Rigby Magnum" but this is NOT CORRECT.

The correct bullet weight for the rifle you're looking at should be stamped on the barrel flats.
I would not attempt to shoot the rifle at all untill you are certain which load the gun was originally chambered for.
The cartridge case is the same for both the 400-350 and the 350 No2 but there is a big difference in bullet length between the 225 grainer and the 310 grain bullet and hence there could be a big difference in throat length for the two chamberings.
Chambering a 400-350 cartridge with 310gn bullet into a gun built for the 350 No2 could result in the longer bullet becomming wedged into the rifling due to the shorter throat meant for the 225 grain bullet and this could raise the pressure to unsafe levels.

If the price is right, the gun is tight, and the bores, throats and chambers are all good, I wouldn't be too concerned about the pitting unless you are after a gun in top condition for a collection.
If you are after a shooter and the rifle has the Rigby name, it sounds like a good find, so long as the price reflects the condition.
Hope it all comes together for you!