Which one is correct ?
His biggest problem is his inaccuracies.
His biggest problem are his inaccuracies."

The main actor or subject of the sentence is 'his biggest problem', and this is singular. So the verb in the sentence should agree with the subject. The second actor, the object, is the plural term 'his inaccuracies', but the verb doesn't need to agree with this.

So it's all a question of agreement. In English, the normal word order is subject, verb, object.

My cat (subject) climbs (verb) trees (object)

The verb should agree with the subject, not the object. So cat and climb are agreeing - my cat climbs. But even first language users of English sometimes have a problem when the sentence has more than one clause - and here's an example.

My mother , but not her friends, is coming to dinner. We might be tempted to say are coming to dinner. But you don't have to because the verb should agree with my mother . The not her friends section is just additional information.