How could she leave out muslim faith one
It doesn't belong with the others because it is probably true in some sense. The ones she mentioned were, like hers, genuine, simple slips of the tongue which don't really mean anything.
Obama's "my Muslim faith" slip was, instead, a parapraxis (aka Freudian slip). These are different because they reveal a subconscious or hidden thought, intention or truth.
Put in different terms, gaffes/slips of the tongue like the number of states, switching North & South, etc. are data errors. They can be caused by a number of factors, e.g. genuine uncertainty as to fact, stress, confusion due to fatigue or sensory overload(mental static), etc. They can be funny or embarrassing, but they don't really mean anything.
Freudian slips, OTOH, are a result of the mental conflict arising from things repressed or concealed. and they can be very revealing. Examples of this include repressed sexual tendencies(e.g. latent homosexual urges), or love/hate conflicts such as in abusive relationships, or even "spiritual" conflicts (this may be the case with Obama, given his life history).
Bottom line, best to leave out the "muslim faith" example because it contains too much truth.
That wasn't a gaffe, it was a moment of clarity.