Typos in Statement of Purpose of PhD application.
How significant a typo is rests largely on the purpose and the level of competition. If you were being considered for a prestigious fellowship, typos in the statement of purpose could and have been used as reasons to screen people out of the competition (because there were too many strong candidates).

For traditional admissions, on the other hand, while such sloppiness cannot help you, it's not normally severe enough issue to disqualify you, unless the typos become so numerous that they interrupt the flow of the writing.