Referring to the episode "One-Man Wrecking Ball"
In this episode, Kat nonsensically throws Monica's name around. I'm not going to explain the issues of bringing a name up without actually following through with it. As important as it was for Monica to bring Kat's name up, she should definitely have been more subtle about it. Tina told Monica, then Monica went straight to Kat to confront her. I realize that Tina could easily have been lying, and maybe Tina's edit makes her seem more trustworthy than she might come off as in real life. However, using the information we are given, Monica should have bit her tongue. If Monica wants a war with Kat, which she expressed-she says something to the effect of: I need to get her out, before she gets me out-than she should fight like a general.
Monica should have quietly campaigned with Vytas' help against Kat. By letting Kat know there's a conflict, and that Monica is aware of it, Monica relinquishes the element of surprise, and gives up the chance at a really clever blindside. Too many times contestants will hear their name, get paranoid, and run crying to the entire tribe. If it were me, I wouldn't.
I would have bit my tongue, rallied Vytas and Tina, which she did anyway, and I wouldn't have told Kat anything. Because, although it worked in her favor, this time, by allowing Kat the chance to defend herself, she lessens her odds of success.
Use the element of surprise, and eliminate Kat while Kat still thinks she's in control over you. It'll be seen as an early power play; it'll eliminate Kat, but it'll also weaken Hayden (since he no longer has his strongest ally). Whereas now, Monica (atleast in her edit) comes off as the Dawn (Caramoan style) of her season, and the drama queen. What if CBS loses it, and actually thinks of a duel Kat can win? If she returns, there's going to be a lot more material for Kat (and Jeff) to use against Monica in terms of 'motives, and she said he said' sort of stuff.
In summary, it worked out for her this time, but she could've played significantly better, and it might hurt her if she gets further into the game.