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?