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***.
You’ve been given several functional words. 
Here are a few more colorful ones:

> 
> ***[airhead](http://www.merriam-webster.com/dictionary/airhead):***
> 
> 
> a mindless or stupid person
> 
> ***[scatterbrained](http://www.merriam-webster.com/dictionary/scatterbrained):***
> 
> 
> having the characteristics of a scatterbrain
> 
>     ***[scatterbrain](http://www.merriam-webster.com/dictionary/scatterbrain):***
> 
> 
> a person who is unable
>  to concentrate or think clearly
> 
> ***[clueless](http://www.merriam-webster.com/dictionary/clueless):***
> 
> 
> not having knowledge about something : unable to understand something
> 
> ***[confused](http://www.merriam-webster.com/dictionary/confused):***
> 
> 
> unable to understand or think clearly
> 
> 

***Bemused***, ***bewildered***, ***disoriented*** and ***flustered***
are the past participles of
***bemuse***, ***bewilder***, ***disorient*** and ***fluster***,
respectively; they are all approximately synonyms for ***confuse***
(so the ***-ed*** words are all approximately synonyms for ***confused***). 
Definitions are all from Merriam-Webster.