From that I've seen in admissions processes is that your overall GPA WILL factor into your application, so DON'T deceive yourself otherwise.
If you look A+++ in the field, but your overall GPA is crap (because you slacked off completely in your gen-ed, some non-related electives or another major that you switched out of), it might mean that the department has to petition the "graduate school" to accept you (at various institutions that I know of, these cutoffs are from a 3 at the least to a 3.5 at the most). A lot of departments wouldn't really want to do this. That's a bare cutoff... something you CAN look up for the various institutions you are interested in.
... But there are subtle factors too. In the committee I was on, we had a mathematical formula (which I won't release) that factored in GPA in the major, overall GPA, subject GRE, general GRE scores, quality/reputation of the undergrad institution, etc. and a "reader's score." The readers score would, in part, try to rectify any noticeable deviations from the "perfect" numerical scores by noticing things like improving performance in upper-level coursework, a GPA negatively affected by the things you mention above, etc... and try to further quantify positive things such as research experience and publications. The reader's score could strongly influence rank. But at the end, the formula ranked applicants, and we made offers to the top-ranked applicants. Formulas (and processes) vary by department... but having a poor overall GPA will probably negatively influence things, and how much you can "make-up" for it by other positive factors depends on how the program committee weights that factor... and of course the relative performance of the other applicants in the pool.