Photos are by the back, the front, obverse of coins, reverse of coins, the error. I’ve never seen an error like this one and it’s not the coins. It’s the case they came in. Absolutely no markings on the outside of the cardboard box the proof set came in. The error is the on the inside of the cardboard. United States Proof Set 1988 is printed on the inside, not the outside. And nobody noticed this at the mint? Has anyone ever seen this? Does anyone have one of these?
The printed die cut was loaded into the folder upside down. More than likely, a full stack was loaded upside down, making that entire stack of boxes inverted. It's also possible that the box is unique. A realistic scenario is when a manager gives a tour to outsiders, picks a printed die cut up off the top of a stack waiting to be folded / glued, explains how the process works, and then sets it back on the stack inverted before continuing the tour. If someone else comes up with another example of the same year, I'd stop hoping for the latter, and claim it to be the former.
I found a packaging error on a 2012 mint set last year. Here is the post if you have interest. 2012 US Philadelphia Mint Set - Packaging Error | Coin Talk
I saw that when you posted it. Neat find but I doubt it would bring any extra. Kinda like mine in this post.