Word/phrase for copying down incorrectly

I immediately thought of typo but that doesn't include the possibility that Joe incorrectly believed it was a 1 that he saw—and so deliberately recorded it as such.

A more appropriate word is mistranscription.

[Merriam-Webster]

: a mistake in transcription : an incorrect copy
// an unlikely word that was probably a mistranscription

And from Merriam-Webster's definition of transcribe itself:

1 a : to make a written copy of
b : to make a copy of (dictated or recorded matter) in longhand or on a machine (such as a typewriter)
c : to paraphrase or summarize in writing
d : write down, record

You can use miscopy:

to copy incorrectly:

• to miscopy an address.

(Dictionary.com)

Miscopy is also a noun meaning: an incorrect copy

From A Companion to Paleopathology 2016:

It might have been a genuine word of the time, or a miscopy of the manuscript due to scruffy handwriting.

From The Greig-Duncan folk song collection :

"Heary peary" at 1 1 .3 is probably a miscopy of "Heavy heavy".

and from Handbook of American Indians North of Mexico:

The designation of this mission as “Purísima Concepción de los Asinais'' came from a miscopy of the word “ Ainai'' in Mem. de Nueva España, xxv II, fol. 163