Idiot, no. Competent ruler, again no. There are a lot of characteristics that are necessary to be a competent and successful ruler. Cersei does not lack for basic intelligence, or even education - there are several scenes wwhere she explains historical events or political developments or long-dead "players" to people who are ignorant of them, so it is clear that she has had at least a decent education and basic, possibly even higher than average, intellect.
The problem is not that Cersei's brain doesn't function properly; the problem is that she doesn't use it. She knows the history of Westeros, but seems incapable of applying its lessons to her own actions. She allows her passions and prejudices and fears and arrogance and sense of entitlement to inform her decisions - which are quite markedly made on the spur of the moment in most cases - and that it her downfall every time.
The reason she seems to do better with someone "more intelligent" guiding her actions is not necessarily that the advisor is smarter than she is. It is that they get her to stop for a minute and THINK. When she actually pauses and takes the time required to consider an action all the way through, weighing its pros and cons and possible outcomes, she often makes the wiser decision. It's when she hatches ideas born of anger or fear or vengeance, and then pursues them diligently without giving them any further thought (beyond how to force them to happen), that she creates one disaster after another. An idea pops into her head, and if it suits her more base and destructive characteristics and goals, she goes full steam ahead with not a thought for flaws or possible holes in the plan.
If anyone had ever taught her self-restraint or self-control, or logical problem solving skills, or managed to get the concept of "look before you leap" drummed into her pretty skull, she would probably do just fine at achieving her goals. Which, frankly, is a rather terrifying thought. Westeros should probably thank its seven gods that no one ever taught Cersei how to perfect a plan before executing it.
I would say she is rather poorly educated: Jon Snow who lives up in the North and was the bastard son, yet he knew that to alienate the Iron Bank was a stupid mistake. Arya who also lives up in the North notes that she reads High Valyrian (in AFFC) and also notes that Sansa, was better at her in every subject except maths.
From this we can infer that both of Ned Stark's daughters read High Valyrian. Yet Cersei gives no such indication, though Tyrion does.
As someone else said, the thing about Ossifer Plum is just something teenaged girls would remember.
There could be several explanations for this lack of education:
cultural: Tywin, failed to educate her because she was female, so Cersei received an education similar to Sansa's (which seems to have consisted mainly of learning good manners and romaunts*).
Now Cersei, whilst she can be charming, is actually quite ill mannered (since as Sansa demonstrates, much of what consists of 'good manners' is actually ironclad self control). So I would say that Cersei was one of those people who delibaretly ignored her Septa/primary teacher: I am sure you all knew someone like this at school: the person who didn't study and also made life miserable for other people, yet whenever attempts where made by teachers to discipline them, this person's parents would come to the school to defend their perfect darling angel. /bang.gif' class='bbc_emoticon' alt=':bang:' /> /ack.gif' class='bbc_emoticon' alt=':ack:' />
Of course this works out to the child's detriment in the long term, since they end up learning nothing, nor do they learn how to interact with people.
Anne Bronte's "Agnes Grey" actually described such children from the governesses perspective, and I think Cersei was rather similar to the girls described in "Agnes Grey".
So not only was Cersei's education poor to begin (due to her gender) but she also failed to learn whatever useful lessons that her poor education did offer (namely that the art of being female is controlling ones every impulse).
As to why I think she was unwilling to learn from her Septa, and furthermore in her years as Queen, failed to pick up a book and read about history, much less apply those lessons onto her political situation.
I would argue that this comes down to emotional dysregulation/borderline personality
disorder with narcissistic elements rather than having a low IQ. I would say Cersei's IQ is about average.
I think that unless your IQ is very high, I doubt that learning is its own reward. So for children with an average IQ, the incentives for learning are A)pleasing parents/caregivers, /cool.png' class='bbc_emoticon' alt='B)' /> not being embarrassed in front of their peers, in later adolescence c) career oppurtunities. The first two, involve earning the love of other people and I would say stem from empathy, which Cersei, like most Lannister's seems to be quite low on. Furthermore Cersei's narcissism (a Lannister trait) compounded by her social position meant she really didn't feel the need to please her teacher by being likable, whilst the fact that she was the only beautiful daughter of Tywin Lannister meant that Cersei didn't feel the need to be studious** to gain the friendship of her peers (of which she had few of anyway), nor does she seemed to have liked her peers much to begin with. I would say this narcissism could be an explanation as to why Cersei didn't feel the need to pick up a history book in later life: she felt she was too special, beautiful, important, clever etc, so that nobody else had anything useful to teach her.
So whilst her narcissism meant that she failed both to learn what was useful in the education that is offered to Westerosi girls, namely socialisation-leading-to self-control, and to self educate in later life, thus making up for the deficits in female specific education.
Of course her lack of empathy meant that she failed to read people properly.
I would say the emotional dysregulation meant that self-control was harder for her anyway (and the narcissism meant that she felt she had no incentive to learn self-control). Of course it lead to all her other silly mistakes: her paranoia leading her to persecute Margaery, her collapse on the night of the blackwater (where she was outdone by a 12 year old girl), her nastiness to Tyrion leading to his alienation, her all-good/all-bad view of Jaime, thinking that sex as a weapon actually works (it doesn't unless the man is your husband or a 16 year old boy).
So IQ is neither here nor there, but personality disorder certainly a huge weakness.
*which were btw often written in verse, which I think makes them harder to comprehend but easier to memorise.
** Remember that Cersei's studies didn't consist of boring maths, physics, science or other socially alienating subjects, but would've consisted of religious education, good manners, music, poetry/literature, which I would say serve to make socialisation easier, rather than harder.