I recall watching a movie in the mid to late 80s with my dad. I only remember one scene, where the monster (with fins on it's back, and had a tail, I believe) attacks a woman at an art or history exhibit while another couple watches. They comment how "realistic" the scene is, before realizing it's the real monster who has been terrorizing their city recently. I also recall it was somewhat of a slapstick monster movie. I swore they called the monster "fin-thing" but I haven't been able to find anything online about it. Help?

The Host? It sounds amusing so if this isn't the right answer please post when you find it.

The Runestone (1991)
From IMDb:
A Norse runestone is discovered in Western Pennsylvania. The prophecy upon it tells of the Norse great wolf Fenrir aka Fenris and that its release from the stone will bring about Ragnarok~the end of the world. Archaeologist Sam Stewart and wife Marla find it has some connection to their friend Martin. A young boy named Jacob is haunted by terrifying nightmares of what is to come, and his family explains these dreams through stories from Norse legend, which says that the only one who can destroy Fenrir is Tyr, the Norse god of war, who is prophesied to return to fight the creature.

QUOTE:
Art Lover: [as Fenrir trashes a Performance Art installation and starts eating the performer] The trouble with this kind of art is that you can't collect it.

The Runestone (1991) - IMDb