Catelyn Stark is one of the most controversial characters of the whole franchise, and in a side-discussion over at the Tower of the Hand I got into an argument with user mirdad, which merits a bigger response, so I used this to let you all take part if you so desire. His argument, edited for clarity:
My main beef with Catelyn is that she doesn't have political savvy in the "real" world. She is like Sansa with the "well, no one would violate guest rights" style of thinking. I have a great question, who was winterfells master of whispers? Who was keeping an eye on the queen during Roberts hunt? not even to spy, but just as a courtesy? Why were the Lannisters not under close watch the entire time? Why didn't Ned have his agents infiltrate all corners of Kings Landing before he arrived? They thought themselves above the game and they got played. Being the man means you have to get your hands a little dirty, I get that Ned and Cat were noble and trust me I loved them at first. But as the series has unfolded we see how hopelessly outgunned they were as far as intelligence gathering and spycraft was concerned. That's my whole point about Jeyne, yeah that wasn't necessarily Catelyn FAULT but damn northerners get your king a few camp followers. A 16 year old after a battle is going to put his dick in something, they should have controlled the something. It's that fantasy of nobility, the "my son is noble and good, and pure, and he is already promised to another' yeah, cuz Ned would never have done that right? oh wait, you raised his bastard after he did the same damn thing. Alleged bastard anyway. This is all viewed through my lenses of having a mother that guided me through the complicated ugliness that is life and death and politics with a deft hand, so Catelyn has always represented that naïve woman over her head surrounded by sharks and thinking she is going to survive with breathing through a straw and reading the good book. [...] I'm conflicted about my feelings on the matter, but it really has bugged me since my first reading. [...]So, let's go at it.
First, of course she has redeeming qualities. She's a great and loving mother, very open-minded about her children and giving them their freedom as well as restraining them. Just look at them. None is spoiled or damaged even remotely like so many other kids in this series.
Second, no one has a Master of Whisperers save the king, especially not Winterfell. What would he report about? There is no large court and no city at Winterfell that would merit the gigantic expense of such an institution. And make no mistake, the Master of Whisperers in King's Landing is effectively a court spy.
Third, why did no one keep an eye on Cersei? Because she's a guest and the queen and the situation has enough tension as is. They basically divided the castle, giving a part over to the king and his family and their many, many retainers. Besides, Jaime and Cersei tricked their own retainers, so how another one no one would trust anyway change the equation?
Fourth, you're utterly mistaken about Robb. He fought several battles without putting his dick anywhere. It was only when he was wounded that an opportunity arose, and he only took it because of the life-shattering event of Rickon's and Bran's death. Without this intervention of fate, he would never have slept with Jeyne. Catelyn was right to trust him, because she raised a true lord. Robb is more responible with 15 as Edmure or Robert are with over 30.
Fifth, Catelyn is everything but naive. She has an incredibly sharp view of political situations and is an excellent judge of characters, save for the people she personally cares about (Littlefinger and Edmure, especially). Some of the most sage counsel in the whole series comes from Catelyn.
Sixth, the deck is stacked against her and the Starks because Martin simply WANTS this to happen. Look at the incredible odds of all of this happening. In 99 out of 100 cases, the Starks are fine. These are odds that any insurance agency would love to have.
Seventh, jumping to Ned, he didn't send anyone into King's Landing to scout because it's not his style. He doesn't have anyone who even can do this (just look at the mess of Cassel's "secret mission" with Catelyn) and wouldn't even know where to start. He knows nothing about King's Landing other than it's the capital and he hates the place. He's also not thinking that he needs to do so because he has the king and his Small Council on his side, which is stacked by Barristan Selmy, Stannis and Renly - all honorable and/or enemies of the Lannisters by default - and knows not to trust either Littlefinger, Pycelle or Varys. He's pretty save on these counts, and point six applies to him as well. His tenure as Hand would have been succesful if Martin hadn't wanted him to fail and crafted an incredibly elaborate timeline of events that ensured his downfall.
To elaborate on all of these matters, I highly recommend Steven Attewell's rereads of AGOT and ACOK. He makes all these arguments in length and backed by textual evidence.