One of the complaints I see often is that the whole Uchiha Massacre could've been avoided if the Third Hokage had just met with Fugaku and talked things over, and a lot of people say it's just a giant plot hole that they didn't, and it was all really because the massacre has to happen for the sake of the plot of Naruto, so the characters are doing things that don't make sense, yadda yadda. But is there any valid explanation for why the Third Hokage wouldn't talk to Fugaku?
I can actually think of two reasons the Third Hokage would avoid meeting with Fugaku.
#1 Political Reasons
One of the Uchiha's earlier grievances was how Fugaku, who distinguished himself during the war and earned the moniker "Wicked Eye Fugaku", was passed over for Fourth Hokage. More insultingly, he was not even considered, with Orochimaru being the only other person whose name was mentioned. Even after the Nine-Tails incident gives the Uchiha greater problems, they do not forget the insult done to Fugaku.
Given how vocal the Uchiha are for their support of Fugaku, I think we can safely assume the Third Hokage knew how they wanted him to be Hokage. In this case, it would be extraordinarily awkward to meet with Fugaku to talk things over. Any sort of official meeting would give Fugaku legitimacy to his claim to the title of Hokage! In fact, it may even stir up the Uchiha more if they get impatient. The sentiment might be something like, "You've recognized Fugaku, so why haven't you announced him as your successor yet?!" And if the Third Hokage happens to die? Things might get quite chaotic, and a civil war would be likely. Having increased the legitimacy of Fugaku, the Uchiha might actually attempt to stage a coup and assassinate the Hokage.
Okay, let's stop and think. Things might be fine if Fugaku really was announced to be the successor. Does the Third Hokage want Fugaku to be Hokage? Would he be okay with that if it would pacify the Uchiha? The answer is a resounding no.
After the war, the Third Hokage resigns to satisfy those saying he messed up. But he handpicks Minato Namikaze to be his successor as Fourth Hokage. According to Danzo and Orochimaru, the Third Hokage chose Minato because he intends to keep ruling the Hidden Leaf with Minato as his puppet (this is in episode 349, I believe).
I honestly believe it is the case that the Third Hokage intended to use Minato as a puppet, at least to some degree. Minato is quite young after all, and young leaders tend to get manipulated. The Third Hokage has a vision for the village and he believes things will go smoothly if the village continues to be run his way. Danzo and Orochimaru have a different vision, which the Third Hokage believes he must stop at all costs. Minato is the perfect proxy, a young man quite sympathetic to his own vision, especially when compared to Danzo and Orochimaru.
And where does this leave Fugaku? The Third Hokage would absolutely never want him to be Hokage. Fugaku, like Danzo, has a different vision for the village than the Third Hokage. With his primary concerns being with his own clan, it's somewhat doubtful he would even be able to see the big picture when it came to ruling the whole village. He might even abuse the position to enrich and empower his own clan at the expense of the village, creating political instability. Additionally, unlike Minato, Fugaku has no ties to the Third Hokage, so the Third would not be able to control him at all. Even if Fugaku does somehow prove to be a good leader, he would not do things the same way as the Third Hokage; he would not continue with the vision the Third Hokage has for the village, and this is greatly undesirable.
Given all this, it is understandable the Third Hokage would not want to meet with Fugaku.
This still falls under the first reason, but the Itachi light novels make it clear Danzo wants the Uchiha to plan a coup so that he can fulfill his long-held ambition of wiping out the biggest threat to village security. Because of this, it is probable he would try to manipulate the Third Hokage into believing meeting with Fugaku is not a good idea, possibly by the very same reasoning I'm using above. When you have an agitator trying to increase strife between the Uchiha and the village, this is a possibility. Thus, even though speaking with the Uchiha is surely a sane approach to lowering tensions, when the Third has Danzo whispering in his ear, you get the seemingly insane approach of publicly ignoring them until things get as bad as they can get. It's not a plot hole, it's crazy by design, because Danzo always wanted Itachi to kill all the Uchiha!
#2 Fugaku's Sharingan
Meeting with anyone with a Sharingan is a giant security risk. With it's potent genjutsu, the Third Hokage would have to worry about being manipulated. He trusts Shisui, obviously, but he also has knowledge of Shisui's power, which is not a good thing here. Knowing a Sharingan exists that can manipulate someone without them even knowing would make him a little paranoid another Sharingan might be able to do something similar.