The tablets can only be targeted when a player gets within close proximity of one, though they do show up on widescan near the bottom of the list above any NPCs and Field Manuals.
The tablets do not automatically spawn when it is time; they only spawn when a players comes within 15'~ of them. Same for widescan. They will not appear on widescan until a player has spawned one by coming within proximity of it.
There is a 2-3 second delay from when a player comes within proximity of a tablet and it will become targetable and scannable, making it easy to miss with enhanced movement speed.
It is possible to search for mog tablets while remaining mounted on a chocobo. 
A message will be displayed to every player in areas subject to Super Kupowers whenever a tablet has been found.
There is a short delay between discovering a tablet and being able to receive your reward. If you warp back to Ru'Lude Gardens too quickly, the Explorer Moogle may talk to you as if you have not discovered the tablet. If this happens, wait until the message telling you the tablet has been discovered appears on the chatlog again. The message you get upon discovery is to notify you, the second message logs your success with the Explorer Moogle and you are then able to receive your reward.
If you already have a reward item marked from a previous Mog-Tablet recovery and the reward given from a new recovery is the same, you will be unable to obtain both the item and the Kupofried's Ring even if you do not have a ring in your possession already. You must first discard the conflicting item, then talk to the Explorer Moogle again to recieve both the item and the ring together.
When all 11 tablets are discovered, Super Kupowers will be granted to all players for one week within certain areas. After this period of time, the tablets will be scattered again, and following a period of 8-24 hours, they will become discoverable once again.
A message will be displayed to every player in areas subject to Super Kupowers when the Kupowers fade away and the tablets spread. This message does not mean that the tablets are once again immediately findable; a random period between 8-24 hours is required.
These are the map locations where tablets have been successfully located. There have been confirmations from multiple servers of matching coordinates. There are, however, many that are yet to be discovered.
When the coordinate is given, a quadrant is also provided to help the search.