Fran complains over the phone that she only got 5 of the 6 boxes of Butter and Herb flavored Rice A Roni that she was supposed to get. A moment later when Mr. Sheffield comes in, there are 6 boxes instead of just 5.
Toward the end, Fran has three piles of rice boxes: two with 6 and one having only 5 rice boxes. However, in the next shot, we see the pile with 5 now have 6.
In Final Jeopardy, the third place player would show their response first, before the second place and first place players. The producers had Fran, who was in third place, show her response last, so as to build up to the surprise that Fran was right and wins.
When Fran gets the Daily Double, she rings in to answer it. The contestant who finds a Daily Double does not need to ring in, as they'd be the only one allowed to answer it.
18 Rice-A-Roni boxes do not constitute a year's supply. That's not quite 1.5 boxes per month. A year's supply would be 365 boxes.
Why would Fran get 18 Rice-A-Roni boxes? She was the winner, she won $200 and would have been supposed to return the following week. The Rice-A-Roni was always the losing contestant's parting gifts. (Anyway, product placement for The Nanny.)
In Final Jeopardy, the person in third place is never last to have their response shown, they are always first.