I am aware that the Beta gate becomes the main gate (post replicators). I'm only a few episodes past that. I noticed in the groundhog day episode that the origin symbol isn't correct (assuming they still use the beta gate). Is there a reason behind this or is it just a goof that seems to keep happening?
According to the SGCommand wiki site's article on the Beta Gate, this was actually Earth's original stargate as constructed by the Ancients. The so-called "Alpha Gate" which SGC had been using before was actually transported to Earth by Ra, thousands of years ago, and later unearthed by us.
That means the "Alpha Gate" was originally designed for use on a different planet (I don't think we know which), and this is why it has a different origin symbol. The origin symbol on the Beta Gate is the "real" symbol for Earth.
Of course, dialing the Alpha Gate while it's on Earth still works as long as you're dialing the correct address. The reason O'Neill and Carter couldn't dial home in the episode where they first discovered the Beta Gate is because these devices were too close. They're meant to operate at interstellar (or at least interplanetary) ranges, and so won't form a connection to another gate on the same planet.