There are at least 5 common browsers and usually at least 3 different release versions of each in use at any given time (this is low balling actually, it could be more like 100 variations). Add to this all the settings which can change amount of memory, whether cookies or java are enabled, flash or silverlight. IE8 is relatively new, under a year, thus the reason it offers a compatibility mode. And programmers are just people, not perfect. If this is the only website that gives you this error then it is extremely likely it is the coding of that site along with your browser and security settings.
Have you tried accessing the site with another browser like Firefox, Google Crome, or Opera? Do you run any anti-malware / script protection that you could disable and then try? Do you block any websites with your hosts file?
You might also try emailing the website administrator.
