Let me rephrase your example:
A company creates a product which they claim to be packaging and selling in packs of 4. Someone buys the packaging also believing there is 4 items per pack and it's shipped to them. The buyers and the company realize there was an error and only 3 items are inside each pack.
Company to buyers: "Sorry, common mistake, we both believed there was 4 products included but we couldn't deliver what we claimed and you believed it. We're just as much at fault for that now that it's shipped and we paid for packaging and delivery. Since we both made that mistake on assumption of the package's content and we can't undo those shipments, it would be fair to share the loss."
That's correct. If there is equal fault on both sides, then the losses have to be split somehow. To make your example perfectly analogous, say it's 1,500 pounds of cherries that are purchased. By mistake, the seller only loads 1,200 pounds of cherries on the truck and also by mistake, the buyer erroneously confirms there are 1,500 pounds of cherries on the truck even though there aren't. In that case, they have to fairly split the damage from their common mistake. It's inequitable to make the buyer pay for 1,500 pounds of cherries and take 1,200 just because he mismeasured given that the seller mismeasured too. But it's also inequitable to make the seller cover 100% of the damages from the incorrect loading given that the buyer made the same mistake.
Your proposal would not hold in any jurisdiction that I know of. If they made a claim to deliver 1500 pounds for 3000$, they would have to deliver what was claimed or otherwise refund the money which was given based on the claim they would receive 1500 pounds which didn't occur. If someone doesn't deliver upon his claims, he's always at fault for making claims he could not deliver on, not the ones believing their claims. Although maybe you simply do not agree with the common practices. Which would be fair enough, everyone is free to have their opinion.
They didn't "make a claim to deliver 1,500 pounds for $3,000". Please read it over again. They agreed to deliver "the 1,500 pounds of cherries we agree are in the truck", something that does not exist.
And common mistake has to hold in pretty much every jurisdiction. There is no other choice. You can't make the seller deliver and the buyer accept the 1,500 pounds of cherries in the truck because there are no 1,500 pounds of cherries in the truck. "Enforce the contract as agreed" is ambiguous because it could equally well mean the buyer has to take whatever is in the truck even if it's not 1,500 pounds or the seller has to put more cherries in the truck -- and neither is what they agreed on.
It would definitely not hold in most jurisdiction. The buyer never made the common mistake of not delivering or causing the incorrect delivery. They did not cause the loss either. They made the error of believing the seller would deliver on his claims.
You now insist that to be analogous to Patrick's situation, we must add it's a common mistake because they accepted upon delivery that it was correct, but when people agreed to Patrick's statement, no delivery was made yet, Patrick was simply making claims as to what he'd deliver and people paid afterward, expecting later delivery as claimed. They couldn't acknowledge it was properly delivered before Patrick returned funds/covered the loss/his debtors paid him/proved where they used funds. They acknowledged the terms of delivery trusting the "seller" (Patrick) to deliver on those claims. They never checked the delivery content and acknowledged to have received what was expected yet. They could only make such a mistake on returned funds.
Nevertheless, even if they did confirm the delivery was properly done when it wasn't and then realized it was not, the seller would still have to provide the goods paid for in full. In the example, even if the buyer acknowledged correct delivery, this acknowledgement did not create any damage/loss. Assuming they would have realized right away there was a mistake, the seller would have to provide the missing goods. If they make a mistake on being delivered properly and realize it wasn't, it only delays the seller providing the goods in full to correct his mistake. The bad report that goods were correctly delivered NEVER caused the seller to not send the goods in full and/or lose part of them. The seller is fully responsible for that. The buyer assuming the full goods would be delivered as claimed by the seller which assumes the same thing neither makes the buyer responsible for the error.
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A common mistake would be if the buyer was for example in Washington (D.C.) and the seller was in Washington (state) and was equipped to deliver in Washington (state) only. On call, both assumed they were in the same Washington when making their contract which ends up being impossible to be delivered before the cherries spoil. Since the buyer also caused the loss through his mistake because both parties did not correctly specify their exact delivery location / delivery zone, he could be judged at fault too and expected to share the loss's cost because the supplier acquired the cherries and they're spoiling. Yet seller could be considered just as much at fault for claiming he was delivering in Washington but not specifying if it was the state or the city. The common mistake of not specifying the exact location directly rendered the contract impossible to execute and caused the loss.
If the seller claims to have something he can deliver an he could execute the delivery if he's right, it does not constitute common mistake. The contract is solely impossible because the sellers fact were wrong and the buyer expected them to be right. It is akin to the seller claiming he delivers in Washington D.C. when he never could. Or someone claiming he could repair something when he does not have the knowledge to. Someone claims he'll deliver X and delivers Y. Patrick claimed to not be exposed when he was. The fact the buyer assumes the seller's statement to be right does not cause the loss or invalidates the contract because the seller could execute it but did not actually have what he claimed, then the seller is fully at tort for not delivering. If someone claims to deliver something in a contract, he's the only one to blame if he did not have the means to. Still, pirate exposure is not even included in the contract to start with which further invalidates that as a potential common mistake. (See further below.)
Common mistake applies when the mistake cause the loss. Not when the mistake is that both believe their would be delivery without a loss while the seller and deliverer was in charge of delivery and the means to do so, and ended up failing to his promises.
(I am no lawyer and unless mistaken, you probably are not either, so feel free to object to these statements/provide further input. They are based solely on my general knowledge and my understandings of the concept.)
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Generally, common mistake applies if the contract is about something that doesn't actually exist or doesn't exist as contemplated in the contract whereas cross-claim is used when it's possible to enforce the contract as agreed yet that leaves one side harmed by the other's mistake even where the mistake is common. To an extent, common mistake is redundant. If execution of the contract as agreed is impossible, you don't need common mistake to invalidate it. If execution of the contract is possible despite the mistake, the common mistake would constitute a cross claim anyway.
This case is on the border somewhere -- it's hard to tell whether it's possible to enforce the contract "as agreed" because the terms are insufficiently precise. This is one of the huge advantages of written contracts over verbal ones. If something unexpected happens, the written contract usually gives you a resolution. However, it often also tends not to be a fair resolution. (For example, in the case of the misweighed cherries, the contract likely would say that the seller's written acceptance of the load waives claims that cherries were insufficient. Though this is a precise resolution, it's hardly fair to let the seller 100% benefit from his mistake while the buyer bears the full costs.)
Here's an interesting thought experiment: Say in that discussion, Patrick was asked this question: "Say it turns out that despite your best efforts, lots of people are borrowing from you to invest in Pirate. And say Pirate stops making payments and many of your loans go bad all at the same time. You probably can't enforce them in any court of law, so your chances of collecting on many of those loans would be low to non-existent. If that happens, are you and your wife going to make personal financial sacrifices to pay back all your investors 100%? This is a serious question and if this happens, I plan to hold you to what you say now and make it a term of our agreement. What will you do?"
What do you honestly think his answer would have been?
Aye, but we're going back to the fact depositors were not investing in Patrick's business or receiving a share of the profits. They were loaning him funds against interest and for safekeeping (financial services) and were led to believe Patrick operated as a bank (Offering said services and Patrick making a profit for himself with the business (the difference between the deposit rates and lending rates.)
The non-exposure to pirate was never part of the contract or included in it and cannot be invoked as a common mistake. Patrick offered a straight "- Deposit money -Receive x% interest" (The actual contract) accounts and operated as bank. The fact people informed themselves about the service provider's practices and declared they liked what they were told does not put any responsibility on them.
As for your thoughts experiment, I personally believe the answer would be "No", which doesn't mean others would assume the same thing or ever received this answer which would make that clause valid.