The pros, first of all. An email user does not expect any interactivity. Moreover, the interviewee has all the time to answer the questions, can reflect about it, and thoroughly explain details. Email is great for research interviews, dealing with complicated or controversial matters. And remember, you can protect your sources and yourself by encrypting the messages with PGP .
Email also has a few shortcomings.
Among them is of course the time delay between the mail containing your interview, and the mail from your interviewee. Moreover, nothing guarantees that your mail will be answered promptly, and in some cases it might be unsure whether it will be answered at all. A lot of people receive such large amounts of email every day that they have to choose which ones to open and read.