Modern digital cameras will compensate for things like vignetting or distortion when shooting JPEG, but if you're shooting RAW, you'll see it. Some cameras, like Fujis, correct in-camera for RAW, too. Photoshop's raw converter has a large library of lens corrections programmed in for most modern CaNikon glass.
Get to a zoom range much broader than about 5X, though, and either deal with a bunch of distortion or spend a lot of dough on a fairly big lens with a lot of complicated glass in it. There are bunches of reasonably inexpensive and compact kit-grade superzooms with 10X or greater focal length ranges but those tend to have pretty inferior optics. The few good ones are large, heavy, and spendy affairs, like the 28-300mm f/3.5-5.6L IS for Canons.
The problem with my recent infatuation with old Olympus Four Thirds DSLRs is that while there are a couple fairly compact zooms in the 5X range, the 14-54mm f/2.8-3.5 and 12-60mm f/2.8-4 (equivalent to 28-108mm and 24-120mm), all the Oly 4/3rds superzooms are inexpensive budget lenses. And Oly lenses are old enough that there aren't any built-in distortion correction profiles in the Photoshop lens library.
There is a solution, though: Leica engineered a superzoom lens for Panasonic's 4/3rds line, the Leica D Vario-Elmar 14-150mm/F3.5-5.6 ASPH./MEGA O.I.S., a mouthful of abbreviations and jargon that basically means "it's about as low-distortion and non-vignetting a superzoom as we could manage."
Back when they were new, they ran about thirteen hundred bucks and were never common, but they occasionally pop up on the used market and I managed to snag one finally.
It may have a slower aperture than the 12-60mm f/2.8-4, but with a full-frame equivalent focal length of 300mm on the long end, this one can get squirrel photos or that motorcycle going past on the far side of the street with ease.
.
