I have been trying like the dickens to collect at least ONE Mysterious Mr. Gnome, but without any luck.  The Mysterious Mr. Gnome is not to be confused with the garden gnome which you can purchase in Buy mode.  He is only available through mysterious means.

The Mysterious Mr. Gnome moves around your property at night when no one is watching.  Even if you wall him in without a door so that he (theoretically) cannot escape, he will vanish from that spot and reappear at a location of his choosing.  Mysterious Mr. Gnome has been spotted inside refrigerators, frozen in a Russian squat dancing pose beside the stereo, pointing in horror at a Death Plant, and more.

How do you get a Mysterious Mr. Gnome?  If you have a Sim on the Criminal career track, sometimes they will bring home stolen Mysterious Mr. Gnomes.  In fact I read one forum post by a Simmer who said that "by the time my Sim got to level 10 on the Criminal career track, I was practically drowning in the things."

This is why I decided to send my Sim on the Criminal career track.  And yet, no luck!  In fact, although I had given her the Kleptomaniac trait, she did not do very well as a criminal.  She only brought home one stolen item, and that was a hideous set of vertical blinds.

(We did have fun stealing things in public, though.  Her yard has amassed quite a collection of giant statuary that way.)

Another way to obtain a Mysterious Mr. Gnome is through fishing.  If you have a Sim who has fished for very long, you may have noticed that they occasionally fish out items which are not fish.  I have collected several guitars, Ducksworth of Bathington rubber duckies, scented candles, bubble bath, and other random items.  But no Mysterious Mr. Gnome!

The third way to obtain a Mysterious Mr. Gnome is by exploring the catacombs beneath the mausoleum.  Since this is a pretty scary (and maybe lethal?) experience, I have only put my Sims through it once or twice.  (Okay, three or four times.  Maybe five.   No more than six, I swear!)

Fourth and finally, sometimes when you send off ore or gems to be smelted or cut, they will be returned in a mail with a note to the effect that "This item was actually a Mysterious Mr. Gnome in disguise."  I still hold out hope for this route!  

One of my Sims had enough lifetime happy points to earn a Collection Manager.  This thing is a real life saver!  Go to their inventory (backpack) tab and click on the Collection Manager, then choose between "ore and gems," "insects," and "seeds."  Now switch to the Town Map view, and voila!  The items you selected will be highlighted on the map with a blue icon.  

When you zoom in on the item's icon, you will see that the game has additionally put a huge sparkly glow on the item, to make it super easy to find.  Collect as many lumps of ore and gemstones as you can, then click on them in your inventory (backpack) tab, and send them off to be smelted or cut.

Hopefully you will have better luck than I have!