The exhibits I counted as “observed” were either large objects; fossilised dinosaur bones, stuffed animals, large machines - or delicate objects; sea animals, stuffed animals etc.
I noticed that where an observed exhibit was behind glass, people stood to look at the object on display. Where an observed exhibit was more accessible - e.g. it was behind a low fence or a rope, people tended to move around the exhibit but not stop. This might have been particular to the types of things that were on display, or a factor of how busy the museum was, but it didn’t feel that way to me - it was as though the less accessible something was, the more attractive it was; the more it was worth pausing for.

For me, exhibits with shallow interaction are the ones where the actions I’m asked to perform as a visitor are very simple (pushing a button) and where the fact that it’s me performing them doesn’t really change the experience. If you push the button or I push the button - the action is simple, and the experience is similar or the same for both of us.
What I noticed about these exhibits was the lack of patience, or maybe persistence, exhibited by visitors where the interaction felt “trivial”. One exhibit in particular featured castings of grave-goods found in caves; bones and other objects laid out in a sequence - with a video-wall explaining the objects. The video was controlled by a button beside each object. I watched lots of people of all ages come into the exhibit - push the first flashing button - wait a few seconds, and then leave. It was as though the payback from the interaction didn’t really encourage people to stick around, even though the content was great (“oh, it’s just a button”). A deeper interaction would have maybe engendered more commitment, more persistence, and maybe more engagement with the content.
The last type of exhibit I took notes on were what I’d call “participatory” - that is where the visitor was asked to contribute something of themselves (e.g. a photo of their face) to be integrated into the exhibit.

I watched people queue for 5+ minutes to have a snapshot of their face taken which was then processed to show what they might have looked like as early humans. Visitors could then send the processed image to a friend via email.
Basically, this exhibit was like a mirror at a funfair - you get to see yourself as you ordinarily can’t. I couldn’t tell if it was this that attracted people to the exhibit, or if it was because putting them into the exhibit made the content more relevant. I suspect it was a bit of both. Maybe this points towards people not really wanting to engage with an experience (especially when content is hard to grapple with) unless it is made personally relevant and shareable? I’m not sure.
The quality of the exhibits at the NMNH is unbelievable; the design, content, physical construction and placement of each item in the museum are really first class.
Watching people interact with the exhibits reminded me that the unobtainable can be more attractive than the attainable - out of reach is intriguing. “Easy” is not always good; encouraging more deliberate, more “difficult” interactions can pay off in the value that the user puts in their experience. Also, you can never really go wrong by putting people in front of a mirror :)

My experience over the past few weeks in Nepal and India has highlighted a similar relationship between curiosity and effort. Many popular attractions, for example The Taj Mahal, offer a fairly easy viewing experience, from getting there to paying your monies and having a stroll around. Of the hoards floating through, very few stopped to inspect anything in great detail, regardless of it being by far the most expensive attraction to visit. It would seem that cost is not so much of a barrier, and not much of an incentive to obtain value for money.
Contrast this to a small, remote temple that requires a dusty four hour bus ride, or a steep hike up a hill at dawn to simply marvel at a stunning view. Both involve far more effort, but for the fewer numbers that do it, the reward is appreciated more.
Just to clarify, develop the point on Shallow Interaction - “A deeper interaction would have maybe engendered more commitment, more persistence”. I think my point is more that the relationship between the content and the purpose of the interaction needs to be thought through. The answer might be that *no* interactivity would offer a better experience - a compelling story and fascinating objects, but no buttons.