Applying for graduate programs, will missing classes count against me?
It's probably inappropriate to say it always "count against you," but it is fair to say that it will be taken into consideration.

For instance, some schools may not admit you officially to the master's or doctoral program in a field if you are missing classes normally expected of students in a given program (for instance, if you're missing analytical chemistry and applying for a chemistry master's). In still other cases, you may be admitted to a program, but with no allowances actually made for the courses missing—that is, you'd be expected to pass the graduate-level courses just like everybody else enrolled in the program.

On the other hand, if you are missing too many "core" classes, then you will probably find yourself struggling to gain admission, since the admissions committee may (rightly?) feel that you have too much prior work to make up.