I didn't have a big problem with the Littlefinger/Cersei scene. It was a mistake by Littlefinger to be so bold, but he was thrown off his game by Cersei's belittling of him, pointing out that his family is only a generation removed from dirt and that he wasn't good enough for Cat -- both sensitive subjects for Littlefinger. That he lashes out and we see him make a rare misstep is an improvement from the books in my opinion, where Littlefinger can be almost unbelievably clever sometimes.
My complaint with the scene is my general complaint with the entire episode, which is it was too rushed and they were attempting to squeeze so much into one hour that the material didn't have room to breathe. It was like "Kill him -- wait!" a split second later, with no opportunity to build any kind of tension because they had to move on to other things. I was surprised by some of the things from the book they didn't have time to include. In particular, Tyrion's taunting of Cersei after he reveals he's known all along about her incestuous relationship is one of the funniest parts of any of the books and somehow it didn't get included.
I wasn't sold on the handling of the introduction of Stannis either. His letter should have been treated as a major plot point, but it's rushed through incredibly quickly, and it's treated so insignificantly that the Small Council apparently doesn't even meet to react to it. I would have preferred the letter was introduced in episode 2 and given more attention, but I guess they wanted it in the first episode so they could tie it in to the murder of Robert's bastards. Lightbringer didn't seem very impressive, and non-book readers might be confused to think it was just an ordinary sword. I'm also confused as to how Cressen hoped his attempt to poison Melisandre would work, since it acted so fast that anyone could have seen within seconds that the glass was poisoned. If Melisandre hadn't been immune to poison, she simply wouldn't have drank it.