When a sentence includes a form of parenthesis—a word, phrase, or clause framed by a pair of commas, dashes, or parentheses—writers must take care that the statement surrounding the interjection is structurally valid so that if the optional parenthesis is omitted, the remaining wording is still coherent. To test whether the sentence’s composition is complete, temporarily omit the interjection, then repair any syntactical and grammatical issues that manifest themselves before reinstating (or restating) the parenthesis.
1. He is considered to be one of, if not the, deadliest assassin in the empire.
This sentence, without the parenthesis, is “He is considered to be one of deadliest assassin in the empire.” This faulty construction demonstrates that the article the must appear in the main clause before the interjection to form a complete sentence, and assassin must be in plural form to correspond with the modifying phrase “one of the” (“He is considered to be one of the deadliest assassins in the empire”); in addition, a repetition of deadliest must be inserted into the parenthesis to form a complete thought: “He is considered one of the deadliest assassins, if not the deadliest, in the empire.” (The extraneous “to be” has been deleted as well.)
2. Effective risk management can help predict—and prevent—major implementation problems from occurring.
In this case, the wording that remains after the parenthesis is excised—“Effective risk management can help predict major implementation problems from occurring”—is syntactically flawed, because “from occurring” modifies prevent but not predict. For the sentence to make sense, that phrase should be inserted into the interjection: “Effective risk management can help predict—and prevent from occurring—major implementation problems.” Better yet, integrate the interjection (with a pronoun standing in for a repeat of “major implementation problems”) into the main clause: “Effective risk management can help predict major implementation problems and prevent them from occurring.”
3. This has not (and should not) prevent smart companies from taking advantage of innovation.
With the parenthesis in this sentence removed, the remaining statement is “This has not prevent smart companies from taking advantage of innovation.” Because “has not” and “should not” must be accompanied by differing forms of prevent, both forms of the verb, one in the main clause and one in the parenthesis, should be employed: “This has not prevented (and should not prevent) smart companies from taking advantage of innovation.”
Note that the three forms of punctuation are interchangeable, although their functions vary slightly: Commas are neutral, parentheses suggest that the information is incidental, and dashes signal information that is divergent or unexpected.
If I may stick my 2 cents in, I think I might revise that deadly-assassin sentence as follows: “He is considered to be one of the most, if not THE most, deadly assassins in the empire.” There are of course other ways to revise it, but I was aiming for less repetition, especially of the word “deadliest,” because by the second appearance of the word, it starts to sound a bit ridiculous, partly because it is hanging in the breeze there by itself (without the word it modifies). I think that the crucial word here is “assassin,” so if I were going to repeat a word, that would be it. But I don’t think it’s necessary, assuming my revision is acceptable.
In your second example, I would also aim for more brevity, and revise as follows: “Effective risk management can help predict—and prevent—major implementation problems.” I don’t think “from occurring” is necessary; I think it’s redundant. But maybe that’s just me.