Can you time travel to get contacts

Here's a list, with the first column being the in-game name, the second being the description of the real piece, the third being a description of the fake:

Ancient Sculpture    A short metal idol                Fake has eyes with pupils.
Animal Sculpture     Two boys suckling a wolf          Fake has one boy.
Beautiful Sculpture  Topless woman with no arms        Fake has long hair.
Great Sculpture      Warrior in yellow                 Palms are facing downward in fake.
Mystic Statue        Egyptian bust                     Fake has a round head, not flat.
Manly Sculpture      Nude man                          Fake has a cloth over both shoulders.
Robust Sculpture     Discus throwing man               Fake is holding a flying saucer.
Valiant Sculpture    Winged sculpture, no head         Fake has bat-like wings.
Amazing Painting     A man in white, and black         Fake, black is left, white is right
Basic Painting       A man with his hand on hip        Fake has both hands on hips
Dynamic Painting     A wave                            Fake has Mt. Fuji under the wave
Famous Painting      Mona Lisa                         Fake has left hand on top
Jolly Painting       A man with a vegi face            Fake has a carrot with green spout as nose
Good Painting        A basket of fruit                 Fake has a fly on the fruit
Quaint Painting      A woman in a yellow shirt         Fake has no white bonnet
Moving Painting      Venus in a shell                  Fake, shell is closed
Supple Painting      Woman in a red kimono             Fake, her head is looking to the left
Serene Painting      Woman holding a white ermine      Fake has a cat instead of a ferret
Scary Painting       An angry man                      Fake has long index fingers pointing right
Solemn Painting      A girl in a white dress, sitting  Fake has a girl standing up and tall
Wild Painting        A black and white figure          Fake has white on right, black on left
Wistful Painting     Women in blue and white bonnet    Fake has an orange bonnet
Common Painting      People working in a field         No fake
Fine Painting        Red dog with two people           No fake
Flowery Painting     Sunflowers                        No fake
Gentle Painting      People in a park                  No fake
Moody Painting       Man with blue plants, crops       No fake
Nice Painting        Red pants, playing flute          No fake
Perfect Painting     Painting of apples                No fake
Proper Painting      Woman with a white collar at bar  No fake
Scenic Painting      Snowy forest                      No fake
Warm Painting        Woman on a bed                    No fake
Worthy Painting      Woman and French flag             No fake

~Source

Alternatively, you can check this gallery here (which is rather too large to directly link each image).

If you want to research yourself, the Animal Crossing: New Leaf Instruction Manual also has a section named "Artists and Sculptors" where it lists the actual name of each piece of art in the game. For example, "Wistful Painting" is *The Girl with the Pearl Earring" by Johannes Vermeer. You could then look the image up in a search engine and compare it with the image ingame.

^{Note: I have the eShop version of the game, so I'm not completely sure that section is in the physical manual.}

During November there will be a mushroom picking event. During this event (whenever it may be), picked mushrooms can be pieces of the mushroom furniture set.

Other than that, the Perfect Mushroom will cause the player to increase in size for a short period of time. As this effect is purely cosmetic, I'd recommend just selling them (except during the event of course).