As I recall, were designed to capture 100% of a star's radiant energy, as energy, while everywhere, is also important to capture. The problem I see as most troublesome with the Dyson sphere, besides stability and gravity, which could be dealt with (spin to provide pseudo-gravity, add ramjets to compensate for wobble) is heat escape-see the Puppeteer homeworld in Ringworld.
Before you ask how spinning is going to help with pseudo-gravity at the poles, it's quite simple. It won't. The poles are devoted to solar energy capture, in the form of photoelectric power generation, tanks of algae (or similar) producing biofuels, or whatever else the constructing civilization finds convenient. The remainder of the inner surface is terraced, so that the ground is always flat, or nearly so, rather than curving more and more steeply as latitude increases. Thousand-mile walls, with elevators built in for transport and airlock functions, keep the atmosphere from flowing down from the higher-latitude terraces to the equatorial terrace-much like the rim walls on a Niven Ring. It is possible that deep oceans with external cooling fins could be used to cool the interior, but I just don't have the thermodynamic engineering to know what-if anything-could be done to prevent the Dyson Sphere's inhabitants from boiling in their own steam.
Not to mention what to do when the sun starts expanding into a Red Giant.
Also unexplained is how we're meant to FIND another species' Dyson Spheres. After all, the intent of the sphere is to trap all the radiation from the sun, so one assumes it would not radiate itself. And, after all, "Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist's, but that's just peanuts to space..." The galaxy is approximately 7.8x10^15 cubic light-years, while a 1AU radius Dyson Sphere is approximately 2x10^3 cubic light-minutes-and there are about 144x10^15 cubic light-minutes in a cubic light-year. This makes for a very small needle, and one humongous haystack.
Mine's the one with the blueprints for a Niven Ring in the pocket.