Some themes use HTML 4.0 Transitional, but WordPress likes to add code for XHTML in posts and pages, so I was wondering if this could be an issue in general. This would most likely not affect your session files problem, so I wouldn't worry about it. The use of an ampersand in php files will cause major problems and may be the culprit in the sessions problem.
Validating your code means checking it for errors in coding. Errors can cause all sorts of problems with web pages, although some errors like missing alt attributes are not a real problem. Your page has some easily fixable errors.