Unfortunately, beginning in 1989, the cross came under fire, thanks to a self-righteous atheist who thinks that because the cross is on public property, it is unconstitutional. In order to alleviate the controversy, the city of San Diego decided to transfer ownership of a portion of Mount Soledad to a private organization, one that wouldn't fall under the jurisdiction of separation of church and state. This, however, wasn't to the liking of said atheist and his lawyers, so they got the state of California involved to deem the land transfer unconstitutional (per state constitution) and started a whole new set of lawsuits and other problems.
In 1998, Mount Soledad was dedicated as a Korean War Memorial, and an attempt to transfer the site to the National Park Service was made. Atheist and lawyers still unhappy... more problems for city and cross supporters. Appropriately, now that it is a war memorial, it is in all likelihood that the Korean War veterans that it represents were Christian, making the cross on Mount Soledad a very suitable monument to the war dead.
The cases are still pending.
The irony of the situation is that this is all happening in the city of San Diego. SAN DIEGO. Named for Saint Didacus of the Franciscan Order. Hmm...
So let's get this straight: an atheist who lives in a city named after a famous Christian files a lawsuit against said city because it has a big cross on top of a hill. Dude... if you're really all about your belief in separation of church and state, then you should either A) sue the state of California for allowing cities named after religious figures or B) move somewhere else (Corpus Christi, Texas, maybe?).
I'm no devout Christian or anything (read my Noah's Ark rant), but I know an asshole when I see one.