Museums probably have to walk a tight line. Give too little information about exhibits and people are not happy, give too much information and people are annoyed as well. Usually, I fall into the first category as I usually go to museums with a specific topic in mind I want to immerse in, such as computing history for example. But even specialized museums on the topic such as the Computer History Museum in California or the Heinz Nixdorf Forum in Germany with their wonderful exhibits offer little in this regard. But as long as there's cellular or Wi-Fi network coverage in the museum, things are far from hopeless.
With a bit of background research one can usually find a ton of information on exhibits on Youtube and Wikipedia, most of it not from the museum itself but from other people. Case in point: When I was recently in Vienna I visited the technical museum because I wanted to take a closer look at the "Mailüfterl", a transistor based computer of the 1950's that was built at the local university. The last sentence is about as much information as the museum said about the exhibit. Quite disappointing but not only did Wikipedia come to the rescue, there are great videos on Youtube with a lot of background information, including this great video tribute made by Google. Wonderful!
Equally, I enjoyed background information about quite a number of other exhibits such as a Univac II tube based computer, a PDP11/40 with integrated circuits, a Powerbook G3 (with a nice 7 minute video of Steve Jobs and Phil Schiller showing how their new product annihilates the competition), etc. etc. etc. And what about that Saba video game console I've never heard about!? The museum doesn't tell me anything about why it is significant but Wikipedia immediately tells me that it's been a re-branded Fairchild Channel F game console that even predates the Atari 2600. What happened to Saba, a brand I know from other electronic products of the 1980s? The museum has no answer, Wikipedia has. Great to find out all these things while looking at the real thing. That's how I like a museum visit to be, go there see the real thing, immerse myself in the details and learn.
Perhaps museums should consider to provide Wi-Fi Internet access and make their visitors particularly aware of it so they can use their own devices (i.e. smartphones and tablets) to get the background information about exhibits they would like to have instead of awkwardly trying to find the right balance between too much and too little, which is impossible to find anyway due to the diverse interests of their visitors.
So you want to bring museums into the 21st Century? I think they will resist losing control over how information is presented in their displays.