To quote from the ever so lovely "Linux Email" book (Reviewed shortly!) ISBN 1-904811-37-X
All three are checked..
The ehlo provided by your email MTA server/client should be it's own fqdn.
So long your ip number reverse resolves ok, the receiving server has no reason to drop you so far.
You may get dropped if the reverse record doesn't match the ehlo hostname. (strict controls)
If you check your reverse dns, you may find your isp hasn't registered your hostname, rather their own.
In which case, change your hostname to match their name, or get your isp to update their dns records to your fqdn domain name.
Checks may also be made against the sender's domain dns A & MX records.
Mail from xyz.com should come from xyz.com's smtp servers..
If both of these records exist, and point back to your fqdn, that's ok.
An A record is the fqdn domain name, and MX is the mail server name.
There may be some more checks using SPF dns records, info at
http://spf.pobox.com/
Then there are the usual block/blacklists and bad recipient addresses etc
Yahoo will only accept mail for it's domains, not for relay.