Peach's description is Mario Party 4 says she's "surprisingly mischievous", which is probably a nod to her reputation as a cheating bitch among fans.
Fan Nickname: The "pity coin" for that one extra coin that gets randomly thrown to someone after some Battle minigames (when the total purse is an odd number).
Keep Circulating the Tapes: The original Mario Party wasn't released on the Wii's Virtual Console, but the second one was. Five bucks says it's due to the issues with the control stick-rotating mini-games. (Of course, it's not impossible that Nintendo could release it on the 3DS, considering how easy it is to rapidly rotate its circle pad using only the thumb compared to the Nintendo 64's control stick, but it's still rather odd to skip to the second installment for a rerelease.
To clarify on this issue, the mini-games that required players to spin the control stick quickly usually had to be done against AI players that can spin the stick a lot faster than a normal person could. People would try to spin the stick with the palms of their hands, which would cause painful blisters if done too much over a period of time. Not only did Nintendo scrap the rotating stick games for future Mario Party titles, but they also will most likely not release the first Mario Party on the Virtual Console unless they change the coding of the game to play those specific mini-games in a different way, which will probably not happen.