Mandy Thompson is quite a complex investigator to take, not only her deckbuilding options but also her weakness seems to have more to it than meets the eye. I am not completely sure, if I am doing it right, but as far as I do understand the rules as written ("When a player is instructed to search for a card, that player is permitted to look at all of the cards in the searched area without revealing those cards to the other players.") the target of the search for certain cards is the entire deck. This is true for the upgrade No Stone Unturned for example. So if you use such a card, than you will always find Shocking Discovery and by that set it of in a "controlled environment" so to say and don't have to worry about it any longer.

Having said that, as long as you do not have found Shocking Discovery yet, than a card searching the entire deck is pretty valuable for Mandy to have. So not only the expensive upgraded No Stone Unturned which you might probably not want to waste on this, but also cards like the 0xp Research Librarian all of a sudden look completely different to me. Even some encounter cards might help, like SPOILER or SPOILER from Path to Carcosa. The latter will also surprisingly be completely canceled as far as I do understand it.

December 31, 2020
To provide clarity to anyone checking this page to ensure they're playing correctly, I will ask:
Is this the correct understanding on how the card works?

• If you draw Shocking Discovery naturally (i.e. Upkeep phase, draw a card action, etc), then you shuffle the card back into your deck. That's it.

• If Shocking Discovery is among the searched cards (i.e. Mr. "Rook", No Stone Unturned, etc), then you discard Shocking Discovery. You cancel the search, shuffle Mandy's deck, then draw the top card of the encounter deck. Shocking Discovery is now in your discard pile.

• If you choose to use Mandy Thompson's ability to "resolve 1 additional target of the search" (ex: No Stone Unturned to search the top 6 cards of your deck and draw 2 of the searched cards instead of just 1 card), and Shocking Discovery is among the searched cards, the entire search is cancelled. This means that you do not draw a card at all because the entire search is cancelled. Then, you shuffle Mandy's deck and draw the top card of the encounter deck. Shocking Discovery is now in your discard pile.

A unique, flavorful, and annoying weakness. Looking at the two elements, the effect and the discard condition, we get:

The effect: only goes off during a search, cancels the search entirely, and you draw an encounter card. Another very situational card. It can wreck your plans or kind of fizzle. I mean, you could build a Mandy deck with no search effects beyond her . You'd be abandoning her ability and signature asset, but you'd also neutralize her signature weakness, making her kind of a bland "generic seeker." That's not a good idea, mind you, but I am not sure there is another investigator who can render her signatures irrelevant, so that's one mitigation strategy....

More practically, you want to find a big search card to draw this out. Like thakaris, I think Research Librarian is probably your best choice to "rip off the band-aid" and get this out of the way early. (I'm also very impressed by their subversion of Treacheries, but, Arkham being Arkham, you would probably draw one of them as your draw from Shocking Discovery instead of before it.) Another strategy is to use Whitton Greene to dig for, say, Segment of Onyx. Since her search ability is limited by revealing locations, it hurts less than searches driven by card play or secrets. Cards like No Stone Unturned (5) are pretty expensive to spend on a wasted action and an encounter card. Depending on your "off class," Mandy has some ability to cancel or redirect the errant encounter card as well.

The discard condition: It discards itself.

All in all, this is a below average signature weakness, maybe even way below.