There are many problems with it. For example, it's not actually part of the SMTP protocol that you have to authenticate, so faked and scam emails are easy to create.
Secondly, it doesn't default to encryption. You have to tell it to do so.
Third, it's got complex and unstandardised rules about detecting origination; there are about five different techniques (for more on which, see my book on amazon). None of the techniques are reliable.
To make matters worse, gmail and others now have a policy of marking mail as spam if it does not come from a large authenticated email provider; meaning that one more or less now has to sign up with a very large corporate, such as hotmail, gmail, etc., to ensure that ones email goes through. And gmail's user interface is terrible, as is the backend. For example, it doesn't actually create folders; it merely 'labels' emails.
Because it's easily faked, fraud and scams are possible, and tricking or phishing are easier to do, because the confirmation of the source is harder to achieve.
Those are just the technical problems.
Then there are psychological problems. So, for example,
1. people don't read it properly, and reply "above" messages, so they ignore a lot of points or respond badly, or miss points.
2. people don't read the tone benevolently; they read it defensively, and get defensive easily. Granted, this happens on other platforms, but because it's not dynamic and responsive like chat protocols, the exchanges get out of hand more easily.
3. people don't understand nice protocols like deleting surplus 'thread', causing mails to get too big; they reply and include original attachments, again sending big messages; they reply-all by default, causing embarrassments; they CC rather than BCC, causing exposure of others' private details, etc.
4. they use it to pressurise you / create stress. It's trivial to send another email, it's not trivial to phone someone repeatedly; it encourages micromanagement and harrassment.
I therefore recommend that people use the social network platforms to communicate, as it forces users to sign up with their actual name and phone number (e.g. facebook, linkedin).