How serious of a mistake it is to accidentally addressed a grad school admissions director as Miss instead of Ms?
I doubt it makes a big difference.
In general, the honorifics &quot;Miss&quot; and &quot;Mrs.&quot; are considered obsolete in professional and academic settings, as marital status is not considered relevant (besides the sexist aspect that there has never been such a distinction in honorifics for men).  They should not be used unless someone specifically requests them.  &quot;Mr.&quot; and &quot;Ms.&quot; have been the standard gendered honorifics for some time, and &quot;Mx.&quot; is coming into wider use as a gender-neutral alternative.
However, I think people realize that these distinctions may be missed by speakers unfamiliar with the language and culture, so I don't think serious offense is likely to be taken.  If you like, you could write a very brief followup email saying something like &quot;I'm sorry, in my previous email I meant to write 'Ms. X'&quot;.
(In general, also note that people who hold a faculty position or a doctoral degree are likely to prefer to be addressed as &quot;Prof.&quot; or &quot;Dr.&quot; respectively.  When someone has both, there may be local customs preferring one or the other, but either should be acceptable.  English does not use both titles together.)