If you think there is a mistake in the transcription/indexing of a record in The National Archives catalogue, or in Digital Downloads you can submit a correction. But it will only be accepted if the transcription is wrong; if it is an accurate transcription of an original record which is wrong in itself, it won't be changed. This was also the practice adopted in the original 1901 census project, which came out at about the same time as DocumentsOnline, the precursor of Digital Downloads. FindMyPast have adopted the same model, while Ancestry will accept all 'alternate' information, regardless of its merits. There are advantages and disadvantages in both approaches.
For what it's worth, I have submitted a number of corrections to the 1939 Register and several of them were updated on the site within a few days.