We first learn about a flaw in Callandor when Cadsuane talks to Rand in the Path of Daggers:
[Cadsune, pg 588 The Bargain]
"It [Callandor] is flawed," she replied curtly, "lacking the buffer that makes other sa'angreal safe to use. And it apparently magnifies the taint, inducing wildness of the mind. So long as a man is using it, anyway. The only safe way to use the Sword That Is Not a Sword, the only way to use it without the risk of killing yourself, or trying to do the Light alone knows what insanity, is liked to two women and one of them guiding the flows."
The reader and Rand immediately think back to two incidents which have happened with Rand and Callandor. The first of these being in the Shadow Rising:
[pg 190-191 The Stone Stands]
Rand pulled his gaze away from her [Moiraine], and it fell on the body of a dark-haired girl, little more than a child. She lay sprawled on her back, eyes wide and fixed on the ceiling, blook blackening the bosom of her dress. Sadly, he bent to brush strands of hair from her face. Light, she is only a child. I was too late. Why didn't I do it [kill the trollocs] sooner? A child!
"I will see that someone takes care of her, Rand," Moiraine said gently. "You cannot help her now."
His hand shook so hard on Callandor that he could barely hold on. "With this, I can do anything." His voice was harsh in his own ears. "Anything!"
"Rand!" Moiraine said urgently.
He would not listen. The Power was in him. Callandor blazed, and he was the Power. He channeled, directing flows into the child's body, searching, trying, fumbling; she lurched to her feet, arms and legs unnaturally rigid and jerky.
"Rand, you cannot do this. Not this!"
Breathe. She has to breathe. The girl's chest rose and fell. Heart. Has to beat. Blood already thick and dark oozed from the wound in her chest. Live. Live, burn you! I didn't mean to be too late. Her eyes stared at him, filmed. Lifeless. Tears trickled unheeded down his cheeks. "She has to live! Heal her, Moiraine. I don't know how. Heal her!"
"Death cannot be Healed, Rand. You are not the Creator."
Staring into those deas eyes, Rand slowly withdrew the flows. The body fell stiffly. The body. He threw back his head and howled, as wild as any Trolloc. Braided fire sizzled into walls and ceiling as he lashed out in frustration and pain.
This episode could be explained by Rand's problem with women dying. If he feels bad about women dying, what must he feel about a little girl's death? Especially one he feels he could have prevented if he had been quicker. Rand is unused to handling such large amounts of the One Power. The feelings of absolute power he has can be explained by this. This whole episode can be explained by Rand's inexperience and emotional stress.
However once Cadsuane tells him that Callandor is flawed, we begin to wonder if that was the cause of the trouble. The second incident we think of occurs in the Path of Daggers:
[pg 526-527, A Time for Iron]
...Flows of saidin spun across the sky, Wind and Water and Fire. Fire. The sky truly did rain lightening. A hundred bolts at once, hundreds, forked blue-white shafts stabbing down as far as he could see. The hills before him erupted. Some flew apart under the torrent of lightning like kicked anthills. Flames sprang up in thickets, trees turning to torches in the rain, flames racing through olive orchards.
Something struck him hard, and he realized he was picking himself up from the ground. The crown had fallen from his head. Callandor still blazed in his hand, though. Vaguely he was aware of Tai'daishar scrambling to his feet, trembling. So they thought to strike back at him, did they?
Shoving Callandor high, he sreamed at them. "Come against me, if you dare! I am the storm! Come if you dare, Shai'tan! I am the Dragon Reborn!" A thousand sizzling lightning bolts hailed down from the clouds.
Again something struck him down. He tried to fight up again. Callandor still shining, lay a pace from his outstretched hand. The sky shattered with lightnings. Suddenly, he realized that the weight atop him was Bashere, that the man was shaking him. It must have been Bashere who had flung him down!
"Stop it!" the Saldaean shouted. Blood fanned down his face from a split across his scalp. "You're killing us, man! Stop!"
Rand turned his head, and one stunned look was enough. Lightnings flashed all around him, in every direction. A bolt stabbed down onto the reverse slope, where Denharad and the armsmen were; the screams of men and horses rose. Aniyella and Ailil were both afoot, trying vainly to quiet mounts that reared, eyes rolling, trying to rip reins free. Flinn was bending over someone, not far from a dead horse with legs slready stiff.
Rand let saidin go. He let it go, but for moments it still flowed into him, and lightning raged. The flow into him dwindled, tailed off and vanished.
This episode can also be explained logically. The One Power is very hard to control in this region because of the Bowl of the Winds. The Asha'men are careful to only channel one weave at a time so they can control it. Rand however is channeling hundreds of weaves at once. There is no way he will be able to control any of them. Rand is so caught up in the power of what he is doing that he doesn't notice that he is not controlling the flows. He tries to stop channeling at the end of the passage, but he has so little control that it takes several moments for him to do this.
Once Cadsuane tells us that Callandor is flawed however, we think that Callandor is what made Rand react this way.
I believe however that Callandor was not the cause of the incidents described above. I have give logical alturnate explanations for these events. I believe that Callandor lacks a buffer, which is present in most other (sa')angreal, to prevent the user from overdrawing on the One Power. Other than this I do not believe Callandor is flawed in any way.
Evidence
If we accept that there are plausible alturnate explanations for the two events described above, then the only evidence we have that Callandor is tainted, is Cadsuane's comment in Path of Daggers. Many people believe Callandor is not flawed because they do not trust Cadsuane. I do not consider this point of view valid until there is evidence supporting it. Let us instead study Cadsuane's comment more closely, as well as related quotes from the series. I have numbered various parts for easy reference later.
[pg 188 The Stone Stands, the Shadow Rising]
6. "Rand pulled at Saidin. Through Callandor... The Power filled him, hammering down like solid thunder. The taint rushed through him in a flood of blackness."
[pg 990, The Traps of Rhuidean, the Shadow Rising]
7. ...through the ter'angreal for one of the two most powerful sa'angreal ever made... And the Power in him surged up like all the seas of the world in storm... The taint swelled as much, curling 'round every particle of him, seeping into every crevice, into his soul.
[Nynaeve pg 122, The Breaking Storm, the Part of Daggers]
8. "Now, don't fear that whoever leads the circle can make you draw too much. This really is a great deal like an angreal. The angreal buffers you against the extra Power, and in somewhat the same way, in a circle you can't be made to draw too much."
a) What is this heretofore unknown buffer? Moiraine never mentioned it, Suian never mentioned it. They have both studied all things related to the Dragon Reborn for most of their lives, and yet they have never mentioned the fact the Callandor is flawed or missing any buffer. So what is this buffer? According to Nynaeve (8), a link prevents a person drawing too much of the One Power, and it is somewhat similar to an angreal in this regard. In (1) Cadsuane says that Callandor lacks a buffer which other sa'angreal have. This sounds a lot like Nynaeve's angreal prevent-overdrawing buffer. Indeed, if a sa'angreal had this it would be 'safe to use'. So this is probably the buffer that Cadsuane refers to. Callandor lacks this buffer. Is this important? Not really. As long as the user is careful, they won't overdraw on the power.
b) (2) is confirmed by (6). Callandor does indeed magnify the taint. The big male sa'angreal also magnifies the taint (7). Is there a problem with this one too? It seems more likely that all male (sa')angreal magnify the taint. After all it seems logical that the more power drawn, the more taint is drawn. So if a lot of the One Power is drawn through a sa'angreal then more taint is drawn proportionally. That Callandor magnifies the taint therefore, isn't really a problem - it's not a good thing, but it isn't a Callandor specific problem.
c) (3) seems to suggest that it is the magnification of the taint causing the mind wildness, not Callandor directly. Mind wildness caused by the taint?... the madness! Yes the taint causes the madness, so Cadsuane isn't telling us anything here.
d) In (4) Cadsuane says that the 'mind wildness' happens when a man is using Callandor, and she goes on in (5) to talk about how a woman can use it. She is insinuating here that the 'mind wildness' won't happen if Callandor is used by a link with women. She doesn't actually say it straight out, but only insinuates it. After all the man is still using Callandor and Saidin, and thus he will still be affected by the taint.
e) In (5) Cadsuane is mostly right. From a) a man can overdraw on Callandor and kill himself, and from (8) link would prevent this happening. So she is correct by saying that using it this way removes the risk of killing yourself. A link would also prevent Rand doing anything insane or stupid with the power, because he is not controlling it. So she is correct when she says that using it this way prevents this.
Note: Cadsuane is wrong however when she says he needs to be linked to two women. He could be in a link of any size, as long as a woman controls the flow to achieve the desired effect.
Summary
The only evidence of the flaw in Callandor is Cadsuane's comment, which on closer inspection contains loopholes for her to be truth twisting. Certainly parts of Cadsuanes comment clearly show that truth manipulation is taking place. Cadsuane also has several motives for convincing Rand that Callandor is flawed. The main one of these being that she is removing from him the ability to use Callandor, and with it his confidence that he can do anything because he has Callandor. This makes him less confident, and thus more pliable by her.
Cadsuane's comment is generally not trustworthy, removing the only good evidence of a flaw in Callandor. Thus I will conclude that there is no problem with Callandor, except that it has no buffer preventing overdrawing - which is not a serious problem at all.