Warning: Wall of text incoming. It's not my fault this show is so dense.
Man I'm still so salty over that. Robb's death is all on Catelyn Stark's stupidity. Everything from her capture of Tyrion, to her release of Jamie, cumulated into Robb losing his life. If she never captured Tyrion, Jamie wouldn't have accosted Ned, and Tywin wouldn't have had to declare war on the Starks to free his son. If she didn't let Jamie go, that Karstark dude wouldn't have had to go and kill those Lannister boys. Which in turn means he would have kept his head, and Robb wouldn't have had to go begging the Freys for troops.
Plus, if she were a better negotiator she wouldn't have had to trade her son's hand to cross that bridge. Her dad was the fucking Lord of Riverrun. The Freys were his banner man. Tell them to open up the gates or else. Stupid Catelyn. She is hands down the worst character to have appeared on this show.
Wait what? Cat had her share of mistakes but lets look at it this way.
1) She didn't just wisk away tyrion, she's had evidence (the dagger, the hair in winter fell, and Lysa's letter). She took him to the veil where she thought he would receive an honest trial because she believed in her sister (and she didn't have any reason not to at that point). Yet regardless of her actions, this movement did NOT start the war.
2) The release of Jamie was also influenced by a couple of factors, not intuition alone. The first is that the Lannisters would have released both her girls if she gave Jamie back (As LF, again, has told her). And when she returned to camp, everyone was so fired up that she knew he would not survive another day as a hostage for Stark. What she did here was a mistake, as I'm sure there would have been better alternatives. But one thing's for sure, it was definitely better than doing nothing.
3) Walder Frey is an ass, and she was wise enough to know it, and she knew any threats would have ended up badly for her son. The freys are not to be trusted, and marriage is a useful tactic in the westeros. She knew they had to move as fast as possible and a marriage to seal the deal seemed like a good plan.
The main mistake she made was trusting Little Finger, and even then her trust in him was justified considering that he once risked his life just to have her. Let's also not forget that she would have been successful in allying with Renly, if it wasn't for Stannis' intervention.
But lets look at the other character who shares most of the responsibility, Robb.
1) Trusting Baylon Greyjoy was an absolue dumb move on his part. He knows what they did, and he was advised against it because they will not forget what Ned did to his house. Yet he still sent Baylon's son (who hasn't seen him in god knows how long) and expect an immediate alliance? WTF?!
2) Regarding the marriage arrangement, it doesn't matter what went down between Cat and frey, Robb consented immediately which made him just as responsible as her in this arrangement. Yet even though he knew his vows he willingly broke it despite cat's advise (again).
3) The Karstark fallout cannot only be blamed on Jamie's release. There are other, more important things to consider. Karstark himself said the war is lost because of Robb's marriage to Talissa, and the fact that lannister children were held hostage in the first place was a mistake that was made due to Robb- Edmure miscommunication. This was not Cat's fault. And when Karstark killed the children he still had a choice. Cat advised him (yet again) to not take his head because they knew the consequences of that. But he did it anyway. Robb losing half his army in the middle of the war was Robb's responsibility completely.
4) With half his army gone. What does Robb do? Go to the frey's, the family he knows cannot be trust AND a family he knows that he has broken a vow to. Cat advised him not to go with this plan but he still went with it anyway (notice a pattern here?).
This is what resulted the red wedding, a betrayal from both banner men that Cat accurately predicted for at least one them. In retrospect, it makes her cautious negotiation tactics wise, not weak.
So yeah, she made some mistakes, but Robb was far more responsible for the red wedding fallout.