It is used to refer to three different feelings.

We tend to avoid using any words with a strong meaning to describe a specific situation therefore, we use おもしろい　for these three different feelings.

1) おもしろい　 be interested in ~
Someone holds attention or curiosity.

In a famous movie about mystery, a main character has a trademark phrase.

If he cannot understand a crime situation, he always says
“I am very interested in this case.”

じつにおもしろい

じつに means really or very.
We would say ほんとうに、とても

A　Japanese movie ガリレオ
https://www.youtube.com/watch?feature=player_embedded&v=j0e60YAXWwg

2) おもしろい　funny
Someone provides fun or causes amusement or laughter.
“He is such a funny person.”
~0:15

https://www.youtube.com/watch?feature=player_embedded&v=CIBWw1Gm8Y4#t=0

I think this guy is regarded as having a good sense of humor in Japan.

3) おもしろい　　unique
It exists as the only one or as the sole example.

“”This commercial is unique.”

https://www.youtube.com/watch?feature=player_embedded&v=WWgt9B_UQDw#t=0

このCMはとてもおもしろいですね。

That’s all.

Are there any Japanese words with have multiple meanings that you have noticed?