Assuming that the code in box 7 of the Form 1099-R for the distribution from the old 401(k) is code G and the taxable amount in box 2a is zero, there would be no change that would be reportable in the numbers on the Form 1040-X. The only thing filing an amendment would do is allow you to provide explanation that the rollover was truly completed in the hope that doing so would preempt an IRS query. You can provide the same explanation if the IRS questions the 401(k) rollover, so it might just be simpler to wait for the IRS to flag the missing information rather than amend. The end result will be the same if the IRS never questions this rollover or the IRS questions it and you subsequently provide the IRS with the information to satisfy them that the rollover was completed.
