The problems with this sentence is multifold.
1) 「どこかに間違っている」 is ungrammatical.
2) There is no respect, politeness or humility expressed anywhere in it. 「聞きたい」 is something you would say to your close friend or someone much younger.
When speaking to a person of a higher status, it is very important not to sound judgemental even if you are 200% certain that s/he has made a mistake. 「どこかに間違っている」, even though it is ungrammatical, sounds highly judgemental. (It would be grammatical if you drop the 「に」 or replaced it with 「が」, but it would still lack all respect.)
The format that I would recommend the most in this case would be to "politely request a recheck" even though you know there is a mistake. To do this, it would often take an extra sentence or clause. Respectful/polite/humble speech tends to take more words in Japanese as in many other languages.
I myself would phrase it like:
The real question, however, is whether or not the rest of your letter would sound equally respectful, polite and humble.