How damaging are writing errors like typos in faculty application documents?
To me, typos in a faculty application suggest one or more of the following:


Detail - you do not pay enough attention to details.
Rigor - you were not rigorous enough to ensure the document is error free by double checking and letting other people check the document.
Importance - if the application was important enough you would have made sure it is error-free, therefore it may not be very important to you.
Culture - you come from a culture where typos are acceptable, and did not bother to adapt.


Having said all that, in the end it is just a tiny factor amongst many more important factors. If you are awesome, this probably won't matter.