Small mistakes in research or personal statement I have recently submitted required documents to apply for a postdoc position. One of the required documents was a personal statement. Unfortunately, after its submission, I found two grammatical mistakes, for example I used present tense of a verb instead of past tense. It does not make a big change in the meaning of the sentence. What do you think about bad effects of these mistakes?
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."