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?
I've assessed thousands of personal statements and train program directors and others in the assessment of such submissions. The first and most important rule is that application packets and supporting documents are assessed as a whole. In that way, inconsistencies are more easily found.
We specifically specify that minor grammatical errors in the personal statement should be ignored except in cases in which proficiency in language is a feature of the programme's entry requirements. For example, say you're applying for a post-doc position in translation studies and, as part of your personal statement, you decide to show off your skill by translating text from classical Chinese to modern Arabic. In this situation, a grammatical error is likely to be considered quite severely.
In my own past, my personal statement contained a glorious error -- I misspelled a common medical term as "Alzeihmer's disease". I'm sure the assessor picked it up. As far as I know, however, it had no effect on my acceptance, progression or accomplishments to date. It did, however, ensure that I've never misspelled "Alzheimer's disease" ever again.
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."