Do admissions care how close a TOEFL score is to the minimum? I work with some students who will attend graduate school in the US. The schools they are applying for list minimum required TOEFL scores. Some have just reached the minimum scores required for admission to their schools of choice. Do admissions departments ever care about how close this number is to the minimum? In other words, will the students be at any greater advantage if they retake the test and get a higher score, or is the "score level met" simply a "met" or "not met" variable that goes into deciding whether or not the students are accepted?
The answer is "sometimes."

Some schools will not care what the score is, as long as you have the minimum requirement that they advertise publicly.

Some schools won't care, even if you don't have the minimum requirement (they may "waive" this requirement routinely).

Some schools will care: they may have one public requirement, and a higher (unpublicized) threshold that they really use in most cases. (Or: the school has one minimum and the department has a higher, unpublicized one.)

Some schools will care: the minimum is required to get your application looked at, but even if it is met they still consider the score in admissions decisions.