The first, and most effective, way of avoiding the HTML errors is to turn off the WYSIWYG editor. What the WYSIWYG editor does is add HTML to your posts for formatting. Normally this would be a good thing, since you don't have to add the HTML yourself. But the WYSIWYG editor that GS uses is horrible coded and doesn't work. It produces crap HTML that leads to the HTML errors you get. Turning it off will greatly improve your chances of avoiding HTML errors. You can turn the WYSIWYG editor off by clicking the Options link(top right of page). In the popup window click the forum tab and uncheck the "Use WYSIWYG editor" option, then click Apply Changes.
Now some of you might want to keep using the WYSIWYG editor, there are still some things you can do to avoid the HTML errors. Most of the HTML errors you will get is because you have unclosed tags. Since the introduction of the wide forums, GS has switched to XHTML strict. What this means is that all tags must be closed, or the HTML isn't valid, this includes one sided tags. For the most part, the WYSIWYG editor closes double sided tags just fine, but it doesn't close one sided tags. So what you need to do is close the one sided tags.
Here is what a two sided tag looks like:

As you can see, there is an opening tag and a closing tag. Here is what a one sided tag looks like:

As you can see there is only one tag. In non-strict HTML the code I just showed you would be a okay, but not in XHTML. The problem with the code is that the tag isn't closed. This is how a closed tag would look like:

That one little " / " is the biggest producer of HTML errors you are going to get when using the WYSIWYG editor. So you have to go in and change this manually. To edit this, you need to get access to the HTML of the post. In the WYSIWYG editor click the HTML icon, this will bring up a popup with the HTML of the post. Go through the post and add the necessary closing " / " You should make sure all one sided tags are closed, the most common tags used are:

Hopefully this tips will help you avoid the HTML errors. These are just tips that I've found to work, there is no guaranteed that they will work for you.