Howard Wasserman explains:
[N]o one takes the presidential oath precisely as written, because everyone adds his name and "so help me God" and omits "(or affirm"). And if those additions/omissions do not matter (a point on which everyone agrees), we have to figure out why transposing the word "faithfully" matters. Paulsen argues, and I think I agree, that the question is whether the deviation (whether addition, deletion, or alteration) "matters," whether it "detracts" from the substance of the oath; presumably that question focuses on whether the deviation from text changes the meaning of the oath. Adding a name or "so help me God" does not; neither does omitting "(or affirm)" (which would make the oath incoherent); and neither would inserting random mumbo-jumbo in the middle of the oath. Transposing a word also does not change meaning--"faithfully" still is an adverb modifying "execute." Replacing a word might not matter if it did not change meaning (say a Jewish President said "Hashem" rather than "God"), but it would matter if it did change meaning (Paulsen uses the example of replacing "faithfully execute" with "probably execute").