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.
No reason for this is ever given in the show.
Out-of-universe, it meant they could keep using stock footage of the gate room and wouldn't have to modify any props.
It doesn't even seem plausible in-universe that the gate itself could be trivially modified in this manner, since everything's supposedly carved out of naquadah.
It is true, though, that it doesn't seem to "matter" in terms of dialing as to what the point of origin looks like; presumably a little reprogramming of the DHD (or gate itself) is all that's needed and away you go. Daniel implies in Solitudes that what it looks like is a fairly trivial matter, and gates are later transplanted all over the place without any adjustment and still work fine, even though per the original lore many of them wouldn't "have" their new point of origin present at all.