Small mistakes in research or personal statement
No one can really say except the one that reads your application materials. Likely it will have little effect, unless the field depends on correct use of language in an essential way. Even there, however, people make mistakes and other people recognize that they do. 

But a good plan for the future is to have a colleague or friend read your materials before you send them to comment on things they find confusing or incorrect. 

You can, of course, send a note of correction if it is in any way important. "I am the king of the world" is a bit different from "I was the king of the world."