There are a few out-of-the-ordinary artifacts in Wapsi Square which have complicated the lives of the characters. Golems, while Lanthian technology, don't count as inanimate artifacts.
Calendar Machine - a Lanthian artifact responsible for multiple time loops. Its original purpose was to halt the aging of some VIPs; unfortunately, it had a problem similar to the Y2K bug which gave it a finite operating period of 1450 years and when it hit its rollover time the entire world reset. It has since been destroyed.
Figurines - Focusing devices used in resolving the Calendar Machine problem. Four stylized figurines made of compressed diamond (only golems are known to do this); when properly held and illuminated they would freeze the holder in place. Shelly had them for as long as she could remember, while Tina had the matching key which would be useful later. There are some open questions. Was there a specific reason they looked like the Golem Girls and Monica, or was it just for art? Is the woman-shaped key supposed to be someone in particular? How the heck did Tina 1.0 get the key anyway, and why did Tina 2.0 feel she needed to keep it safe? We haven't actually been told yet that Bia made them or left them, but she's a likely suspect.
Teleport Tapestry - Long ago it was the default route between Lanthis and Mesoamerica, and almost certainly more complicated than yet told. (The Calendar Machine was hidden at Teotihuacan, a name which has been translated "place of those who have the road of the gods," though the tapestry was found at Yaxchilan) This was very handy, as teleporters have trouble going places they've never been before. Bud destroyed the tapestry when the Calendar Machine was banished into the Demon Realm, to keep it from being used again.
Vimana Cells - Physically small objects used to power the World Grid, origin and method of manufacture unknown. They have at least one alternate use. They are said to contain plutonium; the only explanation of their interior workings provoked reader responses of Radiation Does Not Work That Way.World Grid - A network that keeps Earth sealed off from other worlds, keeping things more or less secure. It's been in place since 4354BC and does not seem to need active maintenance.