I can't speak for music... but forgery in art is not something that is "easy". It generally involves a scientific knowledge of the materials, tools, techniques, etc... employed by a specific artist in a specific time and place. It also involves an ability to mimic or employ materials of the proper age and place. Add to this a technical facility that is often well beyond that employed by many contemporary artists. What is perhaps "easy" about forgery vs the creation of a masterful work of original art is that it is easier to convince a buyer to part with large sums of money in return for a painting he or she thinks is by Rembrandt or Vermeer than it is to get the same individual to part with such sums for the work by an unrecognized artist.
It is actually surprising how museum directors and curators and art historians fall for various forgeries. I think the problem here is two-fold. The museum directors, etc... want to believe that recently uncovered painting X is by artist Y because such discoveries are what makes careers in academia. At the same time... a good many within academia don't really have much of an aye. I am ever surprised at how a bad forgery... or merely a painting by a student of a given master... is taken to have been by master X.
One of the most notorious instances of forgery was that of Han van Meegeren. When art critics decried his work as tired and derivative, van Meegeren felt that they had destroyed his career. Thereupon, he decided to prove his talent to the critics by forging paintings of some of the world's most famous artists, including Frans Hals, Pieter de Hooch, Gerard ter Borch and Johannes Vermeer. During World War II, wealthy Dutchmen, wanting to prevent a sellout of Dutch art to Adolf Hitler and the Nazi Party, avidly bought van Meegeren's forgeries. The same buyers, fearing that the paintings in question might have questionable provenance (ie. have been siezed from Jewish owners) avoided bring in any experts to examine the works. They merely counted their blessings in stumbling upon a brilliant paintint for far less than it was worth. Following the war, a forged Vermeer was discovered in Göring's possession, and van Meegeren was arrested as a collaborator, as officials believed that he had sold Dutch cultural property to the Nazis. This would have been an act of treason, the punishment for which was death, so van Meegeren fearfully confessed to the forgery.
Beyond the political realities of WWII which leant a cover to van Meegeren's forgeries, the artist was also quite astute in mimicking lesser works. In the case of the Vermeer forgeries, van Meegeren did not chose to imitate Vermeer's inimitable mature works... but rather his less-well known and earlier religious paintings.
Even so... looking at the paintings now, it is impossible to imagine anyone confusing these works...
... for a legitimate Vermeer (although the second painting is far more successful)...
There's something almost blatantly 1940s-ish about van Meegeren's forgeries. And this brings us to an issue that just as "our" Beethoven... what we hear and emphasize and stress and value in Beethoven differs from that of the Beethoven of the 1950s which differs from the Beethoven of the 1880s which differs from the Beethoven of the composer's own life time... so it is that a forgery of Vermeer of our time would look drastically different from a forgery from 70 years ago. Both are a form of performance or interpretation of another's work... filtered through the vision or hearing of the time at hand. I suspect that a forgery of Beethoven made today would sound like a horribly bad pastiche in another 50 years.