Trouble sending emails in Apple's Mail Application
Look in the Account settings in Apple Mail and look at the Outgoing Mail Server (SMTP) setting and see if it matches the correct mail service. (i.e. is it using the Gmail smtp server if it is a gmail account. Also, you can use the drop down list and select Edit SMTP Server List to select that particular SMTP server's settings. For Gmail it would be smtp.gmail.com and mine is set to use the default ports, has Authentication as password, and has my login credentials.

Hope this helps.