After Jake and Nog agree to calibrate the EPS conduits for Chief O'Brien they return to the area the Chief had already finished.
Sisko suggests Kai Winn stall for time by telling Weyoun that she needs to consult with Bejor's Council of Ministers, but certainly any decisions about entering into treaties with the Dominion would be the responsibility of the civilian government, and First Minister Shakaar would be directly involved in negotiations.
Jake and Nog have just left Ops when Weyoun has them beamed aboard the Dominion ship. Given the all-but-declared war between the Federation and the Dominion, it seems unlikely that no one in Ops would have been watching for a transporter power signature from Weyoun's ship.
Although the established conversion of Latinum is twenty strips are equal to one bar (Body Parts (1996)), during the auction Quark raises the price of the chest containing the baseball card to one bar, twenty-five strips before Dr. Giger bids 2 bars. Since there are only twenty strips in a bar, this bid is in fact less than the previous bid.
When Jake and Nog agree to complete Chief O'Brien's work for him, Nog says "You calibrate, I'll scan", however, he hands Jake the tricorder by mistake.
Since Jake was part of the Noh-Jay Consortium that earned the five bars of latinum in "Progress" (S1, E15), Jake should have reminded Nog that he wouldn't have the money if it wasn't for Jake's involvement. Additionally, since the five bars were earned in one transaction, Nog's statement that "it's taken a lifetime to save up that much money" is inaccurate.