If memory serves, some of the reasoning for letting customer errors through.
If a possible error in the file or proof is noted by the CSR/Sales rep (whoever is the production gateway) then it should be brought to the attention of the customer. However, once a proof is signed off then it is not the responsibility of the printshop to point out possible client errors. The shop is concerned only with making sure no errors are introduced by the shop's workflow. If the shop starts proofing customer work on press then it is too disruptive to production scheduling for that job, and others in the line, and too costly for the shop to pull the job and/or wait for a customer to confirm that what was noted is indeed a mistake. The customer signed-off proof is the contract between printer and customer and it is the customer's obligation to confirm the contract before signing it off. It is the printshop's obligation to make sure the customer understands the contract nature of the proof and the significance of signing it as OK to go. Knowing this, many shops have a special sign-off tag on their proofs that clearly state the function of the proof and the significance of signing off on it.
I agree, to a point. However, as dabob noted, it is a much more complicated and integrated world out there today, than it was 20 years ago. If you are not looking out after your customer, acting in their best interest, that customer will soon find a smaller shop where they get the attention they feel they deserve. It is no longer just a simple relationship between the printer and the customer where there are definitive lines drawn as to the responsibilities and liability of each. There are too many other entities involved. In today's world it's called "supply chain management". A simple error that could have been stopped at the printer (even though it was not their responsibility) will affect the success of every other entity in the supply chain. For instance, let's dissect the event that started this thread.
Supply Chain:
(1) A professional portrait photographer had to take the picture. It probably took several hours and many many takes to get just that right pose. (2) A professional copy writer needed to come up with the right phrase to capture "the essence" of Trump's presidency. No telling how many hours and phrases got thrown out until they found just the right one. (3) The assembled mock-up probably had to go to whoever in the White House handles Public Relations for the President for approval. (4) The approved portrait with the inscription then needed to go to a printer for production. I don't know who prints them, probably the Government Printing Office or an outsourced printer. (5) about the same time, whoever handles the Library Of Congress's website had to post the item for ordering. There are probably several more entities in the supply chain, but, I think I've listed enough to make the point.
Now, the train jumps the track. A Social Site user (Facebook, Twitter, etc.) notices the error and posts it to the Web. Within seconds, the media picks it up and re-broadcasts it all over the world. Within minutes, who ever handles Public Relations Crisis Management for the President is now meeting to put out the fire. Within hours, the webmaster for the Library of Congress takes the item down from the site, but, the damage has already been done and PR Crisis Management is now working on containment.
So, you see, it's not just a customer/printer relationship anymore. What happens in your print shop affects every other entity in the Supply Chain. Had it been stopped at the print stage, none of the PR fallout would have happened. Do you have to have every person in your shop proof read all pieces. No, don't be ridiculous. I teach my people "JDLR" (just don't look right). They don't have to know what's wrong, just that something doesn't look like it is supposed to. Stop the job, bring it to my attention, or, the CSR's attention, and let them say, "No, it's ok. Go ahead", or, "Thanks! Wow!, Good Catch! That could have been a big fiasco if that ever got out!". Just teach them to be alert, be aware! Don't just be a robot going through the repetitive motions of taking a job order and printing it.
