The spell that frees people from the picture is "VERBAE OMNIS LIBERANT", which is Latin for 'Words free everyone'
The painted desert is a plateau region in Arizona, and is also an allusion to a painting, a work of art and how to describe the different world shown in it.
The same theme of characters ending up in a painting had previously been done many times, including Sunday at the Museum with George (1994) and The Painting (1999). Both titles were filmed in Canada and starred famous Canadian TV actor, Geordie Johnson. In both titles, he ends up being trapped inside the painting for all eternity.
Brian Krause had a brief romantic relationship with guest star Holly Fields years after Charmed ended.
The quiz show Phoebe is watching was called Win Ben Stein's Money and aired 1997-2002. Contestants answered trivia questions through three rounds, similar to Jeopardy. Each round eliminated one contestant. The clip shown would have been from the final round where the remaining contestant went head to head with host Ben Stein to answer the most correct questions in a time allotted.