Once every 24 hours, a daily Mirage spot will appear in Hoenn. The player can also encounter more through StreetPass. At the end of a day, all current Mirage spots will fade away.
In ORAS, a new Mirage Spot will appear every 24 hours. You can also get more Mirage Spots through Street Pass. Also, if I remember correctly, connecting your game to the internet will give you more Mirage Spots, but that might have to do with Street Pass.
In the daily Mirage spot that naturally appears in the player's game, there will always be a hidden item; if a Mirage spot is received from StreetPass, it will not have a hidden item. Furthermore, while it is possible for a hidden item to regenerate on another day if a Mirage spot was naturally received (so long as the area can be refreshed without leaving the Mirage spot), this will not happen on a Mirage spot that was received by StreetPass.
TL;DR: The daily Mirage Spot that you get will have a hidden item. The ones that you get through StreetPass will not. This hidden item will regenerate if you get the same Mirage Spot as your daily Mirage Spot again.
There also a few Mirage Spots, which are listed below, that contain legendary Pokemon, (which are found within a portal generally associated with Hoopa) but you must meet certain conditions in order to access them.
Pathless Plain: Can only be accessed if you have three Pokemon Pokemon with the maximum amount of EVs in your party. On Sundays, Wednesdays, and Fridays, you can find Cobalion through the portal. On Tuesdays and Saturdays, you can find Terrakion through the portal. On Mondays and Thursdays, you can find Virision through the portal.
Nameless Cavern: Can only be accessed if you have three Pokemon that have the maximum amount of friendship/happiness in your party. From the times 4:00 A.M. - 7:59 P.M., you can find Mesprit through the portal. From the times 8:00 A.M. - 8:59 P.M., you can find Uxie through the portal. From the times 9:00 P.M. - 3:59 A.M, you can find Azelf through the portal.
Fabled Cave: Can only be accessed if you have a Pokemon that is level 100 in your party. In Omega Ruby, Reshiram can be found through the portal. In Alpha Sapphire, Zekrom can be found through the portal.
Gnarled Den: Can only be accessed if you have both Reshiram and Zekrom in your party. Kyurem can be found through the portal.
Trackless Forest: Can only be accessed if you have Ho-oh or Lugia in your party. From the times xx:00 - xx:19 of any hour, (for example, 8:15 P.M., 4:01 A.M., etc.) Raikou can be found through the portal. From the times xx:20 - xx:39 of any hour, Entei can be found through the portal. From the times xx:40 - xx:59 of any hour, Suicune can be found through the portal.
Dimensional rifts above Dewford Town: Can only be accessed if you have Mesprit, Uxie, and Azelf in your party. In Omega Ruby, Palkia is found in the dimensional rift. In Alpha Sapphire, Dialga is found in the dimensional rift. If both Dialga and Palkia are in your party, Giratina can be found in the dimensional rift.
Storm clouds about Fortree City: Can only be accessed if you have a Castform in your party. In Omega Ruby, Tornadus can be found in the storm cloud. In Alpha Sapphire, Thundurus is found in the storm cloud. If both Tornadus and Thundurus are in your party, Landorus can be found in the storm cloud.
Crescent Isle: Can be randomly received at the start of the day. It can also be received from a passerby. Cresselia can be found through the portal located on Crescent Isle.
Hope this helps you out! Feel free to ask me any further questions that you may have about Mirage Spots!