What kind of accuracy should we look for in a 338 semi custom build?

Any custom rifle that won't shoot .5 in whatever cartridge isn't worthy of the name. The good ones easily hit .2-.3 and that is my expectation of a custom. There is no such thing as an inherently inaccurate round but some rounds like the 338 WM and 338 RUM do seem to be easier to tune for some reason.

If a rifle won't put the first cold bore shot where is puts the warm bore groups, it isn't the right gun for hunting and it wasn't built right. That said, I have never seen a rifle that shot consistent cold bore POI/POA that didn't group well. A gun that shoots 1" or more at 100 isn't going to cold bore a 5" circle at 800 yards every time.
 
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Any custom rifle that won't shoot .5 in whatever cartridge isn't worthy of the name. The good ones easily hit .2-.3 and that is my expectation of a custom. There is no such thing as an inherently inaccurate round but some rounds like the 338 WM and 338 RUM do seem to be easier to tune for some reason.
This is spot on...

Considering the cost of a custom rifle, I expect consistent .2-.4 moa accuracy. It better be a sub 1/2 moa rifle. My expectations are to have enough accuracy to kill animals out to 1000 yards with confidence. At the range I expect to shoot 5-7 inch groups at 1000 yards to accurately dial in the rifle/load/trajectory.

With a semi-custom (aftermarket barrel installed onto a factory action bedded into a decent stock) I would expect consistent .5-.75 moa.

Of all my accurate rifles, my big 338 is the least finicky to develop a load and also has amazingly low extreme spread and velocity is consistent across groups as well. In steady wind conditions, my 338 will shoot amazing groups at long range, picture below shows a group I shot at 1005 yards with a steady diagonal ~7mph wind. I missed the wind call on the particular group, but it still shows the capability of a good 338 RUM. And this is a hunting weight rifle, 9.5 lbs including optics.
 

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Dean2 how is your 338-378 build going I am on AO. Had I known what I know now I would have gone 338-378 as well. Turned out my bolt face is .580 not .534. I can't complain my RUM is shooting ral well.
 
Dean2 how is your 338-378 build going I am on AO. Had I known what I know now I would have gone 338-378 as well. Turned out my bolt face is .580 not .534. I can't complain my RUM is shooting ral well.
Not done yet. It is a very specialised build so don't expect to see it for another couple of months. How did they manage to build up the bolt face enough to offset that big a difference and what kind of action did you build the RUM on?
 
Dean2 to tell the truth I just got lucky enough that the Weatherby extractor will pull the cases out. About every 5th round will not completely extract but for the most part the brass will fly out of the action. Niether me or the gun smith checked the bolt face. It was supposed to be all from a 270 Wby. It is working and I don't want to mess with it now. Only 50 rounds through it and already getting half inch groups and I haven't plated with but 1 powder RL33. I put a Cadex brake on it and I am very impressed with the recoil reduction. I can't really feel the gun hit my shoulder when shooting it. My Defcom Griz brake is a little more effective maybe but it is on a 300 Wby. The Griz brake actually pushes the muzzle down when shooting off hand. The 2 of them really work like a brake should though.
 
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