If someone says it looks like the 90's they probably mean your obvious use of Tables. All of your "Issues" are in separate table entries with several pixel padding to give them a border. That is just something you really don't see much of anymore.
Next I'd say something that makes the site look a bit dated would be the fact that all your elements are sort of floating around the page with nothing tying them down to a coherent theme. Nowadays most sites have a common theme that anchors all the elements to each other. But all of your various modules, images, text and elements are just there. Floating above the background with no borders, modules or backgrounds of their own to anchor themselves to each other.
You're header isn't really a header it's just text on a gradient background that extends all the way to the bottom of the page.
Put these things together and you have a very dated looking site. But honestly I don't know that much could be done to improve the viewer's experience because the site is very simple and it is very easy to read the comics. If someone is bothered by the look of the site it's probably just a little sniff of criticism because they are the kind of people who need to find fault.
If you WANT to improve your site and make it look more modern then
this weeks feature might be something worth looking into. With fairly minimal effort and expense you could set yourself up a Wordpress site with either the Comicpress or Webcomic plug in and no time you'd have a site that looks like 90% of the other webcomic sites on the internet. This is probably the best route to take if, for example, HTML and Tables you do ok but PHP, Java, Server Side includes and CSS are not exactly your cup of data. Because the site you have created is very simple in terms of what is available on the web these days and to modernize it and make it comparable to what a simple Wordpress site can offer you through its base functionality will require some serious programming chops.
But you should only change it if you WANT to change it. Your son is young and his comics skill will grow considerably over the years. At this stage in his development there is a certain charm to having an old school HTML site displaying his work. It's not like you expect him to be generating massive amounts of traffic and revenue at this point.
I'd say if he gets to the point where he wants to start selling stuff with his designs on it then it will be definitely time to upgrade. If anyone starts to make him feel bad about the look of the site, time to upgrade. But mostly it's up to you guys as to when you want to do it. It isn't a difficult task.
Good luck.
