One major aspect of this Gilded Age transformation that carried into the Chicago World's Fair was the advancement of architecture. Complex, memorable, appealing, and sturdy architecture was sought to be created, and the technology to reach these feats were literally developed as the architects went. The need for these superb feats of engineering was nonexistent until the wave of Gilded Age transformation swept the nation, calling out for larger, more magnificent buildings. In the sense of the World's Fair, however, these buildings were often created for visual, rather than practical reasons, but the same principle applies.
Even with the advancements in technology and industry due to the inflow of inventions and labor of the Gilded Age, many of the engineering insight needed to construct these monstrosities of buildings had yet to be developed or even thought about. As aforementioned, these bridges had to be crossed as the engineers came upon them. Challenges such as these were unimaginable. Not because the laborers expected no problems, but because the rapid wave of Gilded Age transformation left behind technology and necessity not even dreamed of until recent years. With that, the workers moved on as everyone else had to in such a time of rapid change from all angles -social, industrial, etc. And modified as they went.
Challenges posed were usually those of stability. Buildings lacked sturdiness, collapsing in storms or even simply posing the issue of load-bearing capacity. Building massive, usually vastly tall structures without the proper architectural knowledge made them nearly impossible to safely construct, but without the need of such large buildings before, the stability issue was an oversight. One handled accordingly as the issue came up, as mentioned, by developing the means to achieve the feats at the time they were needed. One specifically was the issue with the Ferris Wheel. The massive, multi-ton axle had to be hoisted up, nothing so heavy having been carried so high before, but the obstacle had to be overcome and managed, else the Wheel would never have been constructed.
In summary, the construction of the grand buildings of the World's Fair reflected on a, quite literally, larger scale the issues that had to be overcome during the Gilded Age. With new developments come new challenges.