Does a mezuzah have to be placed exactly at the beginning of the upper third of the doorpost or is it good enough within the upper third?
It is preferable to place the mezuzah at the beginning of the upper third of the doorpost. However, it is sufficient that the mezuzah should be approximately at the beginning of the upper third, and if it goes above this point, this is also fine. It is important, however, to ensure that the mezuzah does not go below the upper third, and that it should not be within a tefach of the lintel.
Sources: See Menachos 33a-b; Rambam, Mezuzah chap. 6:12; Yoreh De’ah 289.