Rule: That cannot be omitted when it introduces an appositive clause.
Examples of errors:
The fact that is a very useful phrase in English, particularly for German learners, since that clauses are not as easily used in nominal functions--particularly as subject--as German clauses introduced by daB:
That he was scatterbrained was common knowledge.
Daß er zerstreut war, war allgemein bekannt.
English prefers to eschew clausal subjects, although they are grammatically acceptable, and it accomplishes this most commonly by extraposition:
It was common knowledge that he was scatterbrained.
If the verb allows it, another alternative is to construct the sentence- with the clause as verb complement, e.g.:
Everyone knew that he was scatterbrained.
Still another alternative is afforded by making a that clause appositive to fact:
The fact that he was scatterbrained was common knowledge.
This construction is particularly useful when the that clause functions as the object of a preposition, when extraposition may be awkward or impossible:
*We must put up with that he is scatterbrained.
*It must be put up with that he is scatterbrained.
We must put up with the fact that he is scatter-brained.
= The fact that he is scatterbrained must be put up with.
An appositive that clause must be distinguished from restrictive relative clauses, in which the relative pronoun that can be omitted. In appositive clauses, that is not a relative pronoun and cannot be omitted. This is true not only with fact as the noun phrase head, but also with other nouns, e.g.:
I got a message that I should leave immediately.
*I got a message I should leave immediately.
There was a report that Daniel had been a thief.
*There was a report Daniel had been a thief.