For what it's worth, Rand was an unusually capable person in her specialty (she wrote two popular, and somewhat politically influential novels in her second language), but still not in the same class as her heroes.
I'm not sure you've got the bit about Rearden right. I don't think there's any evidence that he came up with the final design for the bridge. There's a mention that he worked with a team to discover Rearden metal, and presumably he also had an engineering team. The point was that he (presumably) knew enough engineering to come up with something plausible, and that he was fascinated by producing great things enough to be distracted from something major going wrong that I don't remember.
I have no idea whether Rand knew Galt's engine was physically impossible, though I think she should have, considering that other parts of the book were well-researched. Dagny's situation at Taggart Transcontinental was probably typical for an Operations vice-president in a family owned business. The description of her doing cementless masonry matched with a book on the subject. Atlas Shrugged was the only place I saw the possibility of shale oil mentioned until, decades later, it turned out to be a possible technology.
The research fail that jumped out at me hardest in Atlas Shrugged was the idea that so many people would consider a metal both stronger and lighter than steel physically impossible. By the time the book was published, not only was titanium fairly well understood, it was also being widely used in military and (some; what could be spared from Cold War efforts) commercial purposes. Its properties don't exactly match Rearden Metal (even ignoring the color and other mostly-unimportant characteristic) but they're close enough that it should be obvious that such ...
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.