I recently set up 2-factor auth on my Google account, and then went through the process of adding an application-specific password to everything.
Well, apparently everything but the SMTP entry in Mail got the news. Instead of letting me know, Mail has been trying to use my secondary Comcast SMTP, which sends anything not from Comcast into oblivion. My outgoing emails have been swiftly and silently vanishing away.
But, I tested my outgoing emails by sending to my Comcast account, natch, which worked fine because they were going *to* a Comcast address, instead of *from* a Gmail address. :-P