Generally, you can file 1040 up to three years after the original deadline for filing. So if a person just filed for 2010 (due April 15, 2011) on April 15, 2014 (three years later) and now see an error, can they still amend the return with 1040X? I see this web page at the IRS that seems to say you can: Nine facts on filing an amended return
Be sure to enter the year of the return you are amending at the top of Form 1040X. Generally, you must file Form 1040X within three years from the date you filed your original return or within two years from the date you paid the tax, whichever is later.
However, it says generally and thus I wonder if that still applies in such an extreme case.