Does that mean I should contact my ISP and ask them to update their server?
I wouldn't tell them to update their server. I have dealt with enough technical support technicians over the years to know that would only make them defensive and they are not the ones empowered to make that decision. I recommend contacting them and giving them specific information on what is happening and I would be prepared to tell them the source SMTP servers the mail is coming from and I would also strongly recommend you try another email client on your Mac just so they won't have a convenient scapegoat in Apple Mail. There are some free email clients in the App Store that you could try. At the present time I am using Airmail from the App Store and I believe they still offer a trial version on their
website or you could try the free
Mozilla Thunderbird. Both of those are compatible with OS X 10.8.