Secrets Do Not Help Win Kingdoms
So let me get this straight, King Robert specifically gives all the power of the Seven Kingdoms to Ned Stark until "the rightful heir" comes of age (subtle move there, Neddy boy.) Given all that power, Stark doesn't really tell anyone about the piece of paper he holds until the King dies and Cersei is able to orchestrate the whole audience with Joffrey already sitting upon the Iron Throne.
If someone just named me Regent and Protector of the Realm, I would tell the whole city, proclaim it from every balcony and generally make it very inconvenient for anyone to try to betray me. A King's decree is only worth the power behind it and when Cersei rips the paper decree in two, we see just how worthless Stark made Robert's last wishes by not revealing them to the public.
Take Help When It Is Offered
Shortly after, RENLY BARATHEON offers Ned Stark the troops he needs to secure the throne for whatever heir of Robert's that he wants to install. Sure, Renly wants to be King after SER LORAS has planted the idea so *ahem* firmly, but Ned is a strong enough influence that he might have persuaded the younger Baratheon to stay in line. Instead of taking the "hundred swords" that Renly says he can provide, and striking at the Lannisters while there is still time, Ned Stark spits in his potential ally's face.
This echoes the overtures that VARYS THE SPIDER and Littlefinger have all made in trying to help the Hand, but the honor that Ned Stark holds onto so strongly prevents anyone from taking his side.
(As an aside, the audience has no idea if Stannis is fit to rule or not because we have yet to meet him, but readers of the series know that he's just as stuck on honor as Stark is. Renly's line about good soldiers making good kings certainly rings true.)
Don't Trust the Man that Covets Your Wife
This one is just a gimme.
With all of these missteps, it's not really surprising that Ned Stark goes to the Iron Throne thinking he's got all this politics stuff in the bag only to have his guards be stabbed in the back. We get to see the fallout of who comes out on top now that Joffrey Baratheon will be crowned king.
The Lannisters were the only smart ones and have already prepared two armies to be led by the patriarch TYWIN and his son Jaime. The scene with Tywin butchering a deer as he lectures his son was pitched so perfectly that I nearly wept. I don't care if Tywin Lannister doesn't get much screentime in the coming seasons, Charles Dance nailed that character so well in that scene that he can pretty much coast from here on out. (Plus, I don't know if it was the red cloth and black leather, but I kept seeing shades of Duke Harkonnen from Dune which only emphasized the pathos for me.)
I also love how Tywin compared his house to the Targaryens. He's right in realizing that the family name is the only thing that matters, if you don't have magic blood that is. DAENERYS is slowly realizing that she is touched by forces she doesn't really understand. I can't wait to see what's going to happens when those dragon eggs start to open.