What are the important examples of Julius Caesar's ignorance that are inexcusable? Could these also be attributed to his downfall?
There are many ways to answer this question. I will focus mostly on the religious aspects. From this perspective, we can say that Caesar's actions can be construed as inexcusable.
First, Caesar should have considered more carefully the words of the soothsayer “beware the Ides of March.” But as we well know, Caesar ignores him several times. In the beginning of the work, he simply proceeds with his victory celebration, and throughout the work, he continues to ignore him. This is an important point to keep in mind, because good Romans took the words of soothsayers and any religious intervention as a serious event. Even a cursory glance at Roman literature will show you how seriously the Romans viewed these religious matters.
What is more, there are other prodigies and omens, which are neglected. From this perspective, the gods were warning Caesar and he constantly neglected them. Any Roman would have seen this an inexcusable. Moreover, Calpurnia has a nightmare - more warning that Caesar ignores. The fact Caesar reject these points shows his pride.
Second, it is clear that Brutus and Cassius and others believe that Caesar is aiming at kingship, which would overturn the Republic. Caesar should have known this and acted accordingly. Even when the citizen Artemidorus tries to warn him of the conspiracy, he does not bother. Again, we see pride and ambition.