I wonder whether he was also right in telling me that I should always arrive on time.
I wonder whether he wasn't also right in telling me that I should always arrive on time.
have in common the implicit idea that "he" was right about something else that came up earlier in the narrator's discussion. That's the effect of including also in each sentence. So the question becomes, does the sense of the sentence change at all if you use "wasn't" in place of "was"?
From a purely objective standpoint, I think, the answer is no: Both wordings describe the same thought process and lead to the same possibility that "he" may be right again.
On a subtle level, however, presenting the narrator's wondering thought with the verb "wasn't" implies (to me) that the narrator may once have thought that "he" was wrong about punctuality, but that the previous instance in which "he" was proved correct has led the narrator to reassess that earlier opinion. Using the negatively formed idiom "I wonder whether he wasn't also right" somehow imparts a sense of second-guessing to the narrator's thought that the straightforward "I wonder whether he was also right" does not. At any rate I detect a difference in how the two sentences are pitched, even though their objective meaning is essentially identical.