I had one jury trial and appeal on a unilateral contract formation case and issues like this kinda presented itself. I had to research contract law so much that, based on that research, my gut feeling is that BRS would lose.
In closing arguments to the jury, i used some website contract formation analogs and that was persuasive; the jury came back in my favor in like 30 minutes. Key to the analogs was the person on the internet taking affirmative action to agree to a contract. The jury--and this is a factual question for the jury not a legal question for a judge--was not impressed by thinking they could agree to something just by going on a website.
On the other hand, if evidence of the actual retail price of the GHL products was admitted into the record--and i have serious doubts there because i would object all day long and twice on sunday (extrinsic evidence is extremely hard to get admitted when there is no ambiguity in the contract)--the jury could be persuaded that it was a mistake and take pitty on BRS regardless of the law. Even then though, my jury instructions would make it clear that since the buyer made no mistake, BRS' s mistake could not get it out of the contract.
Last, one person's order itself does not look like a mistake, it looks like a reduction in price by BRS:
Totally agree that this is a hard case to get to a trial or even a lawsuit. But that really just supports the position that BRS is at fault and it is the party that could have prevented this situation entirely with some due diligence.