Mishmash Museum

""Thus ends the Greek artifact/dinosaur/big freakin' diamond exhibit.""

- Mike J. Nelson, Riff Trax edition of Batman and Robin

TV museums tend to be very badly organized. It is not unusual to find suits of medieval plate armor, Egyptian sarcophagi, stuffed grizzly bears, priceless cut jewels, giant cutaway models of the human body, and Tyrannosaurus skeletons all in the same room... which has, in addition, a few dozen Old Masters hanging on the walls and modern abstract sculpture in the corners. Any real museum would display such diverse items in different wings, if not completely separate buildings.

In general, the less time the characters spend in a museum, the more this trope applies. TV episodes and movies with extended museum sequences are more likely to have exhibits properly categorized, as it is more fun to have the characters racing from wing to wing in order to find what they need to defeat the artifact thieves, magically reanimated dinosaur skeletons, or whatnot.

Note that this trope can have a little basis in reality: the very first museums were created to display whatever odd objects that their patrons owned, so they placed different objects together because they were from the same owner. They were often called "cabinets of curiosities", and their intent was often to show the diversity and oddity of the whole world. There are also still small museums who embrace the mishmash, because they don't have enough space or they don't know better.

Anime and Manga

 * The museum in one of the first few episodes of Futari wa Pretty Cure almost avoids this, as it's specifically an art museum with basically just realistic paintings on the walls and a few sculptures. They just couldn't help but throw in a few suits of armor, apparently.
 * You forget that the Metropolitan Museum of Art, for instance, has a very extensive display of arms and armor from around the world, including King Henry VIII's armor and Charlemagne's helmet.
 * Then again, the Met also features furniture and recreations of rooms owned and used by historical figures.
 * Averted in Tokyo Mew Mew, where Ichigo and Masaya's first date is specifically spent in a separate wing of the museum devoted to conservation and endangered animals.
 * Justified in CMB, since the curator is a 12 years old Cloudcuckoolander and the fact that his "museum" only consisted of one big room.

Film

 * Night at the Museum avoided this, as the layout is based on the actual New York Museum of Natural History. (It is a replica, however, because they wouldn't let them shoot it in the actual museum.)
 * It was used a bit in the sequel Battle of the Smithsonian, however, as much of it was set in the interlocking storage basement of the many museums that make up the Smithsonian.
 * Which itself would be Did Not Do the Research meets Rule of Cool (or convenience) as the real storage and research facilities for the Smithsonian are in Suitland, Maryland (above ground), and there are no connections, underground or otherwise, between the Mall museums. Which only makes sense, given the high water table on the Mall, the existence of the Metro system, the fact that the buildings were all built decades apart, and that one of the Mall museums isn't part of the Smithonian at all (the National Gallery of Art is an entirely separate institution.)
 * Aversion: The Da Vinci Code was filmed in the real Louvre, albeit a Louvre that a naked 80 year old man managed to traipse around about half of while bleeding to death in order to rub graffiti behind paintings.
 * As mentioned above the Gotham Museum of Art features exhibits on dinosaurs, diamonds and greek vases all in the same room in Batman and Robin.

Literature

 * Semi-averted and justified in Umberto Eco's Foucault's Pendulum. The opening museum has all kinds of weird stuff in it, including the device of the title, but it is divided into categories. That these categories are rather arbitrary is, of course, thematic. (The periscope is the glassware section and not the optical instruments section, but surely there's some arcane reason for it...)
 * Also justified by being Truth in Television, as that museum exists in real life.
 * The Separate Collection of the Wyrd Museum is like this, but at least there's a reason.

Live Action TV

 * In the Doctor Who story "The Seeds of Death", the Tardis lands in a museum where displays about Yuri Gagarin, Leonardo DaVinci's flying machine, and a futuristic teleporter are all in the same room. On the other hand, this museum was pretty much the work of one person, who probably did have limited funding and space.
 * Though it looks like a mishmash at first, it is explained that it is in fact a single exhibit about the history of transportation - which is what early flying machine designs, the first man in space, and a teleporter have in common that results in them being displayed together.

Radio

 * Radio 4's The Museum of Curiosity allows guests, often comedians, scientists or writers, to "donate" exhibits to the eponymous museum. Exhibits donated thus far include: the pineapple, the P-51 Mustang, a book containing every joke ever told and the Holy grail. Oh, and God, the Big Bang, the concept of privacy and Spider-Man.
 * Also on Radio 4, The Museum of Everything. Exactly What It Says on the Tin.

Western Animation

 * In the first Kim Possible movie, A Sitch in Time, a primitive monkey idol is kept in the same room as an Egyptian sarcophagus and at least one dinosaur skeleton... and a giant fishbowl.
 * The Simpsons parodied this by depicting Picasso and Andy Warhol works on display right next to a Matt Groening sketch.
 * The Looney Tunes short "Louvre Come Back To Me" has Pepe LePew visit the Louvre, where we find artwork that is not (and would not be) in the museum's collection, including Dali's Persistence of Memory, Wood's American Gothic, and some Henry Moore-type abstract sculpture.
 * As a tribute, Looney Tunes Back in Action has a scene in an equally fictionalized Louvre. Basically, the only painting depicted there that is in the actual Louvre is the Mona Lisa.

Video Games

 * Averted in Ghostbusters: The Game, as the Aztec, Egyptian, and Civil War exhibits are kept separate.
 * Averted partially in Grand Theft Auto IV's Libertonian. The museum's lack of space gives out a mishmash appearance, but a glance of its directory shows that it clumps each of its four exhibits into dedicated segments of the building.

Truth in Television

 * Under the terms of Henry Clay Frick's will, his New York mansion was made a museum (the Frick Collection on East 70th Street), but none of the paintings were moved or removed (nor were labels added); thus the works are arranged according to the robber baron's aesthetic sense.
 * the Museum of Jurassic Technology in Los Angeles, California.
 * The Science Museum of Minnesota has an entire exhibit designed this way on purpose. It contains a traditional Hmong house, an Egyptian mummy, a phrenology machine, a giant dead polar bear, and many prehistoric tools, among other things.
 * The Redpath museum in Montreal is home to several stuffed animals, fully articulated skeletons of Gorgosaurus and Dromaeosaurus, an Egyptian mummy, a seashell collection, a mineral collection, some trilobite fossils, a samurai suit of armour, a fossil of an aquatic lizard, Chinese shoes made for bound feet, charts showing the dinosaur family tree and the phylogenetic tree of all life on Earth, an anaconda skeleton, a Triceratops skull, a banner made out of human teeth, skeletons of two whales, a sea lion and a turtle and a giant origami pterosaur, all in about two and a half floors of space. In other words, it looks exactly, inside and out, like every natural history museum stereotype ever. It's Crazy Awesome.
 * The Pitt Rivers Museum Oxford is a Victorian Anthropology museum with its exhibits grouped by function, so the cases of 'things used as currency' are next to the 'Things used as Armour', the Chinese pigeon whistles are near the Hawaiian feather cloaks, and the whole place is dominated by a totem pole.
 * Ripley's Odditorium located on Hollywood Boulevard of Ripley's Believe It or Not! fame.
 * The Greybull Museum out in Wyoming fits this trope perfectly. it has taxidermied animals, historical artifacts, and fossils scattered all over the museums with no sense of organization whatsoever. A fossilized turtle shell is on the exact opposite side of the section with Coryphodon tusks and belimnite shells, both of which are opposite the corner with the sauropod femurs.
 * Hungarian Count Istvan Szechenyi once commented that the National Museum features his father's portrait between a snake and a crocodile - mainly because that's pretty much how the museum worked back then: mainly halls filled with random stuff, without any logic in how they were arranged.
 * Sir John Soane's Museum in London is another excellent example of the 1800s urge to collect all sorts of anything (medieval objects, large and small sculpture, books, stained glass, Egyptian scarabs, various gems et al.) and then just bequeath your whole house to the city of London to remain a museum in perpetuity. Sir John further distinguished himself by creating a catalogue of his holdings on three separate occasions (1830, 1832 & 1835). Thus, the building and its collection are amongst the best-documented in the world. And most importantly: the deal includes leaving all of the objects exactly where Soane placed them when he acquired them.
 * Sometimes happens in special exhibits even when the permanent collections are well-organized; if a patron loans or wills his collection to the museum, it will be displayed together in a "collection of Rich Donor So-and-So" room, rather than separated out by where the art/artifacts came from. Depending on the collector's taste, such exhibits can sometimes be confined to one type of object, but can also be Mishmash Museums.