They might do the same stupid thing Gmail does, and ignore certain characters. My Gmail is "first.m.last@gmail.com", but I constantly get mail from idiots who don't know their own email address, and use my "firstmlast@gmail.com" to sign up for things. This problem would go away entirely if Gmail didn't do this. Facebook might do similar things to make it "easier" to login, even though there are security implications.
That’s by design though, the .‘s are optional. You can add more even. Also plus routing: first.m.last+whatever@gmail.com also routes to the same email.
“ Gmail doesn't recognize periods as characters in addresses -- we just ignore them. For example, you could tell people your address was hikingfan@gmail.com, hiking.fan@gmail.com or hi.kin.g.fan@gmail.com. (We understand that there has been some confusion about this in the past, but to settle it once and for all, you can indeed receive mail at all the variations with dots.)”
> This problem would go away entirely if Gmail didn't do this
No it wouldn't. The problem is that people believe they have addresses they don't. They don't have firstmlast@gmail.com any more than they have firt.m.last@gmail.com.
I have a surname@ address, and I receive similar mails all the time. People just simply assume they have my email address. No dots involved.
It would go away for me because no one ever uses the real first.m.last address; all the misdirected mail is from people who think firstmlast is their email address.