Is there a significant difference in meaning between "Should not be null" and "Should be not null"? Or, maybe, one of the options is wrong?
There is a slight difference.
In the first sentence, not modifies the should and says what X should not be, which means here that X should be anything except null.
In the second sentence, should is not modified. The sentence says that X should be not null. So here you're saying what it should be instead of saying what it should not be.