1. Email delivery latency: depending on the service you use, the time it takes to deliver emails to the user can vary. Worst case I encountered was up to 20 minutes delay when there were issues with Mailgun.
2. Usability: you have to leave your current app and switch to your mail client. You may be on a device where you don't have a mail client installed at all, so you have to provide a password login option as well.
3. The sign in dialog gets more complicated and it's hard to explain to users how it works as it is not all that common. This also had effects on sign up/sign in dialog design which we found to have a negative impact on conversion rates.