Similar to how both universes must remain balanced - a theme that was explored fairly in-depth during Season 3 - there's evidence that the timeline is, to a certain extent, elastic. But only as long as the universe is not interacted with by an outside force - that throws the chain of events out of whack and causes the large divergences predicted by the Butterfly Effect.
Here are a couple known points where our universe was influenced by outside events:
- When Walter first made the window to see Over There
- When Walter took Peter to our side
- When August saved the girl
Likewise for Over There:
- When September distracted Walternate
- When Olivia told Walternate about the "other universe"
- William Bell
In 2x16, Peter, we see September talk to other Observers about the mistake he made, and how he has to correct it. Likewise, August was told that his mistake would be corrected, but he figured out how to avoid that fate.
This suggests that, at least from the point of view of the Observers, both universes have a predefined path. Unless a mistake or intentional change is made, the small differences caused by the presence of the Observers is negligible, and won't cause the timeline to excessively diverge.
On the other hand, any time a universe is influenced by an outside force, unless that outside force takes extra steps to keep the universe on-course like the Observers, that's when things start to spiral out of control.
We were given an example directly by an Observer in 3x10, The Firefly what happens when an outside force influences a universe. In September's own words to Walter, after the example: "You and I have interfered with the natural course of events. We have upset the balance in ways I could not have predicted."
Up until then, the differences between the two universes did not spiral out of control (Even DC's superheroes are largely the same; different color scheme, and Supergirl survived Crisis on Infinite Earths instead of Superman, but all the same heroes exist). Given the same people in similar situations, they will tend to take similar courses of action.
The times they did not, there are some pretty large changes. For example, here's extracts of two lists of some fairly large differences between the two universes, either with regards to the world or the main characters:
- William Bell died young and never met Walternate.
- Walternate had a lab anyway, and went on to found Bishop Dynamic.
There's no indication that Nina Sharp ever existed Over There.
- Likewise with David Robert Jones.
- I'm wrong about Nina, see Season 4. So far, there's still no indication about Jones.
- Lincoln Lee had a very different life.
- The Hindenburg, as mentioned in the question.
- Andrew Jackson either didn't exist, or was never president.
- The Challenger disaster didn't happen - those 7 crew are presumably still alive over there.
- US states include: North Texas, South Texas, Midland, and Dakota (One state, not North and South), among other changes
- Fauxlivia was with Frank Stanton, not John Scott like our Olivia. We don't know if either one exists in the other universe.
- The Hotel Attraction was built Over There.
- Casablanca, The Maltese Falcon, and Back to the Future all were made, but with different stars.
So there are some pretty drastic differences. There is no outside force keeping the two universes on a similar course of events; it's just coincidence due to most people making similar choices between the two universes - Andrew Jackson wasn't president, but someone else was. Those three movies were sill made, but with different actors. Some other hotel was in use instead of the Hotel Attraction. Zeppelins were used instead of Airplanes, which were never invented Over There. So on and so forth...
The only times (that I can think of) where a universe has been pushed into a specific course of events has been by an Observer that was fixing a mistake they made. Otherwise, similar courses of events is the expected norm.