Question: Is there a single-word adjective to describe an office functionary who consistently incorrectly refers paperwork onwards to the wrong internal department in his or her organisation because he or she doesn't realise he or she is wrong?

Answer: 
It would seem that such an "office functionary\*" is either ***untrained***, or, if they have been trained and maybe even retrained, ***incompetent***.
This would be (wilfully) [***ignorant***](https://en.oxforddictionaries.com/definition/ignorant).

> 
> ADJECTIVE  
> 
>  1 Lacking knowledge or awareness; uneducated or unsophisticated.  
> 
> *‘In that way, our people can remain ignorant, uneducated and dumb.’*
> 
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Reference:  

<https://en.oxforddictionaries.com/definition/ignorant>

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Edit (added definition of *willfully ignorant* from **Wiktionary**):

> 
> **[willful ignorance](https://en.wiktionary.org/wiki/willful_ignorance)** ‎(uncountable)
> 
> 
> (idiomatic, law) A decision in bad faith to avoid becoming informed
>  about something so as to avoid having to make undesirable decisions
>  that such information might prompt.
> 
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>