I did already notice a potential one, since in days I will be taking the EB west to Glacier National Park. Which is just west of Williston, ND(and east of Wolf Point, MT, but it's closer to Williston). Anyway the train passes right by the former Fort Union Trading Post, which was once a very big fur trading post between several Native American tribes in this area. Today, it's a national historic site, run by National Park Service. Plus this trading post stands BARELY east of the North Dakota/Montana border, and the parking lot for this place is barely on the Montana side of the state line. So it's funny to think this is a point where once you see this, it's obvious you're crossing the state line between both states!
Thanks to the Glacier National Park website, for pointing out other area NPS ran sites not too far away.
This was on a page, where they recommending visitors who may get fed up with crowds at Glacier, to consider also visiting other NPS sites(even the ones that aren't national parks) not too far away(Grant-Kohrs Ranch in Deer Lodge, MT(between Butte and Missoula), Big Hole National Battlefield in Wisdom, MT(outside Butte), Little Bighorn Battlefield National Monument in Crow Agency(southeast of Billings), etc). Though I'm surprised they pointed out a site as far away from Glacier, as Fort Union Trading Post.
Finally in Minot during the smoke/stretch break there for the morning westbound train 7(though I don't think it's open for eastbound train 8 in the evening), there is a coffee shop and snacks truck that's parked just immediately south of the Minot Amtrak station, where people can walk over to for coffee and/or snacks during that 37 minute(for the westbound train IF it's on time, plus juckins.net makes me think it very often makes it on time and sometimes earlier) stretch stop. Also if you want to try such a quick 6 minute(per google) walk east for a photo op, there is a historic Soo Depot for Minot which still stands today:
https://goo.gl/maps/9faePGThewfUN8MPA (this link is just to show you how to walk east to it, and that it could be done for the length of the smoke/stretch stop there). Pic of the historic Minot Soo Depot there:
https://goo.gl/maps/TzmG1pa6hdBC6Hzu6
The more I explore Minot on google street view, the more I wonder if going there would be worth a potential train trip there someday? It even does have an art museum(Taube Museum of Art) there, which is interesting. Free to visit per their website, and of course they accept donations to support their operations if you want to do so.
Back to hidden things/easter eggs you see along the route, I just noticed two more. One between Devils Lake, ND, and Rugby, ND(both towns east of Minot, this'd only be visible in daylight if you're going west on train #7, but on eastbound #8 you'd go by here after dark). Which is the Lake Alice National Wildlife Refuge, and that you see the western Lake Irvine part of it briefly as you pass through the town of Churchs Ferry, ND. The other thing I suddenly noticed along the EB's route in Montana, was inbetween Glasgow, MT and Malta, MT(closer to Malta btw). Which is that the train passes through the Bowdoin National Wildlife Refuge, and you get a good look at Lake Bowdoin for a brief while, as you pass through this wildlife refuge.
I'm sure the part near the Mississippi River west of La Crosse(where you enter Minnesota), will inevitably be great for scenery as well. I'm sure others could fill in on the Portland and Seattle branches of the EB, where there are great places to see scenery. As I'm only going west from Chicago to Glacier National Park(though once I looked up the area around Sandpoint, ID for fun), I didn't yet look up the route of the EB beyond Whitefish and Sandpoint. I'm sure there are some great scenic points, west of Spokane(where the EB splits into 2 trains)!