Considering that Gmail is unable to connect for sending mail -- and that the guy in Switzerland, who doesn't have access other than to load the website via web browser, can telnet to my SMTP server to send me a mail -- I was assuming it's not my ISP. I just confirmed that by directing my home email client to the SMTP server running on port 25 on a different server on a different host that also uses Postfix and Dovecot.
The Linode domain I'm trying to use is youdolinux.com, and the MX record reads mail.youdolinux.com. The MX record is what I'm pointing my client to, but I don't include the mail part when sending myself mail from Gmail (e.g. I type
myaddress@youdolinux.com and it comes through to the email client at home, which uses mail.youdolinux.com). Since I'm using secure IMAP, setup through Dovecot, I know this works.
Comparing the Postfix main.cf on my Linode to the Postfix main.cf on the machine running on the other host, the only difference (other than pointing to a different domain) is that I'm not using procmail. Since I'm not familiar with email servers, I can try configuring this, but since procmail wasn't pulled in by apt-get when I installed dovecot-imapd and postfix, I was assuming this isn't necessary.