The best date formats are the ones that are (1) clear and (2) familiar to your audience. You want your readers to focus on the content of your resume/CV, and this will be difficult if they have to "translate" dates to a familiar format in their heads while reading.
In general, the two extremes - long, unambiguous dates verses shorter, more informal dates - run the spectrum from convenient to write and compact (if potentially unclear) to longer and harder to write (but clear).
And, the most important thing: Pick a single date format for the document, and follow it everywhere.
Shorter date formats, such as 4/12/10, are familiar and comfortable, but they can be unclear. Did I just write 12 April or 4 December? 1910 or 2010? (That last is unlikely to be a problem in a document like this.) Choosing a date format and sticking with it for the entire document can help with this.
Longer, unambiguous formats are preferred from the standpoint of being clear, but they take up more room (an issue in a resume, especially when formatting them for a single page) and can look clumsy to some audiences.
I'd find out what formats are the most common in your field and use those.
People are generally pretty good at recognizing different formats, but why make more work for them? It's the work of a few minute to change the date formats to be appropriate and consistent.
While it's unlikely that an "odd" date format will cause someone to put your CV in the "circular file", if presented with two resumes that are roughly the same in terms of qualifications and experience, a hiring manager could easily simply choose the one that looks more familiar and comfortable.
I'd avoid dates formatted like "November 2 2013" because losing a space can be hard to read. Using spoken-word-type formatting like "3rd" can be a bit too chatty and conversational in a formal business document (as well as being another opportunity for typos to occur).
In terms of ranges: Most style guides suggest using an en or em dash (not two hyphens in a row) for these.