I was impressed with this sort of flow in the Natural History Museum in Vienna.

If you have a big museum it will certainly work! And as Daniel suggested: visit the NHM Vienna, it is one hell of a big history exhibition (the paleontology part), and the museum always ranks among the top three or so in the world. In the Biology Centre at Linz we have only very little space but try to tell the entire story as well, even if it's just of single topics. Our exhibition on the evolution (and everything else) of cephalopods has just ended. The visitors were most impressed by being able to follow their history from the very beginning of what makes a cephalopod, to seeing old fossils, to evolution (Hox genes etc.), to mass extinctions, to predator-prey relationships, to behaviour and intelligence, and to observe them alive and playful in aquaria (ok, I admit, we also provided yummy squid-recipes). The stories you can tell the visitors make just so much more sense than if you single out any specific subtopic and provide the information in isolation from the big "rest". I believe this holistic approach played a big part in making it our most visited exhibition ever...!

At the Freie Universität Berlin there is an obligatory introductory course for Bachelor students of Geological Sciences called "Paläontologie & Erdgeschichte" (paleontology and earth history), which has been taught for several years. Only recently in the summer term of 2014 it was replaced by "Einführung in die Paläonotologie" (introduction to paleontology) and most aspects of earth history where moved to a course in stratigraphy and earth history.

The first four lectures or so (of 12 lectures) were devoted to the evolution of the universe, planetary evolution and abiogenesis (introducing the concept of chemo-fossils among other things). The rest of lectures in this course presented a very short overview of protorozoic life and was otherwise mostly focused on the phanerozoic Eon. These phanerozoic lectures typically combined information about major orogenic activity, events in the evolution of animals and plants (introducing the groups that are most important as index fossils for that particular Period) and typical sedimentary deposits for each Period against a background of major climatic changes (“hot-house vs. “ice-house”).

That approach offered the students a broad overview of the natural sciences aspect of the “big picture” but given the time scale and limited time in an introductory course in the second term it is understandable that ist mostly ignored the social science side of it. But in the stratigraphy part of the module in the next (third) term links between external forcing (Milancovic bands, sun spot activity) and major developments in human culture would pop up now and then.

I hope this review of an introductory course which I both absolved and taught as a student assistant answers some of your questions, Michael.

The useful thing about "Big History" is that it provides a teaching framework that breaches the natural and cultural worlds by nesting culture within nature.  At Macquarie University where it has been used in teaching for a while, each year the history department would ask the scientists for objects that illustrate the signposts of increasing complexity, ie. a meteorite, banded Iron sample, Ediacaran fauna, vertebrate remains etc. 

Many years ago I did a small exhibition in a university museum on the history of the Earth.  It changed my perceptions about the nature of museum work.  Try capturing 4.6 billion years with only a small number of specimens, it focusses thinking and provokes many interesting discussions.

The "Big History" framework can be presented to people in small spaces and with small collections, it is just more challenging (and fun!).

"Big History" as an exhibition or educational concept indeed works well on a high school level.  In the U.S., the Mount Rushmore National Memorial has served as a source of multiple educational concepts in many U.S. high schools. That memorial, situated in Keystone, South Dakota, consists of four busts, 18 meters high each, of four major U.S. presidents: George Washington, Thomas Jefferson, Theodore Roosevelt, and Abraham Lincoln. These busts were artistically blasted by T.N.T. out of a mountainside by Gutzon Borglum and 400 workers.  These particular presidents could symbolize the birth, growth, development, and conservation of the U.S.  Hence the monument could teach historical events on a grand scale. Moreover, numerous animals and plants lodge in and on the monument, and could provide study of the ecosystem.  

@Daniel R. Brooks: Do you refer to the permanent exhibition at the Vienna museum or the special exhibition named "Time trips – wie kann man zeit zeigen [how to make time tangible]"?

The NHM in Vienna has got the advantage that it includes an anthropology and prehistory section - so it can offer at least some continuity between natural and human (cultural) history in its permanent exhibition. What I had in mind is something concise, i.e. a special exhibition like "Time trips" that illustrates the history of everything without crucial points getting lost under the weight of information.

@Björn Berning: Holistic approaches of presenting a certain topic can be often fruitful and rewarding, especially in the context of museums (which are not constrained by school board plans).

In a way "big history" is related to certain ideas of holism but perhaps the most critical point of big history is bridging the gap between natural history and cultural history (as noted by Andrew Sampson).

@Jens: Yes, especially in the geosciences there are certain university courses that try to provide the larger picture.

At high school level children get taught some isolated parts of the whole picture in the history, biology, geography and astronomy classes but usually not a comprehensive overview. So an aim of museums could be to teach the link between these parts (as a mind-expanding journey).

@Andrew Sampson: Macquarie University has of course the benefit of David Christian and the Big History Institute:

http://www.mq.edu.au/research/centres_and_groups/big_history_institute/

You can log in as a high school teacher and get lots of teaching materials - in English, though, which is a certain threshold for teachers from non-English-speaking countries.

A special exhibition like the one you mentioned is what I had in mind and, based thereupon, a piece of teaching for high schools that can be swallowed in two hours.

@Nelson Orringer: Everyone knows Mt. Rushmore but I wonder about its suitability for big history classes - the monument and its surroundings arguably offer enough objects for the study of both, nature and history, but to address nature and history in a somehow unified way (such as a time scale?) could be challenging.

 You can find in the complexity theory and educational approaches of Edgar Morin this kind of proposals: seven knowledge needed for the future education

http://unesdoc.unesco.org/images/0011/001177/117740eo.pdf

Over several years, the University of Michigan has been collecting data from schools that use Big History, to assess student academic growth and overall perceptions to History. They recently produced this short video, embedded in an article, about Big History instruction at Black River Public School (Holland, MI): https://news.umich.edu/black-river-big-history-project-asking-the-how-and-why-questions/#.WpYSoDLRy5I.facebook and https://arts.umich.edu/news-features/black-river-big-history-project-asking-the-how-and-why-questions/