Well, I could name the most recent controversies:
- A corruption scandal that involves the King's son-in-law, Inaki Urdangarín, and most probably his daughter, Infanta Cristina, as well. In fact, the King himself is involved to a certain degree by trying to hush the scandal and protecting his daughter (who to this day hasn't been questioned). You can read more about that
here.
- The hunting trip King Juan Carlos took, spending tens of thousands when his country is in economic crisis. Not to mention, he was hunting elephants; while it is not illegal where he was, it is morally a very dubious act. And people wouldn't even know about the trip, if the King hadn't suffered an accident requiring a hospitalisation. You can read more about that
here.
- The fact King Juan Carlos was accompanied on that trip - and on many others, by the looks of it - by a woman who is believed to be his mistress. In fact, the King is believed to have numerous affairs throughout his marriage, which may explain why he and Queen Sofia decided not to celebrate their 50th wedding anniversary this year.
In past, the Spanish media always protected the King and didn't report anything that could tarnish his reputation. That is slowly changing. Currently, only two members of the Royal Family are completely scandal free (to the best of my knowledge) - Crown Prince Felipe and Crown Princess Letizia. Queen Sofia's patience with her husband's ways has earned her a lot of sympathy and support as well.