To answer this question, I first took a look at what the research so far is saying, which you can find examples of here, here, here, and here.
However, running form and gait does change a fair amount with barefoot runners versus shod runners. With cushioned shoes the primary issues arise from the lack of our ability to feel the ground and know precisely what we are doing when running.
When running in cushioned shoes we can get away with a variety of bad habits. For example, the cushioning makes landing hard on our heels in front of our bodies comfortable enough to not cause concern for most runners. Called overstriding, this style of running puts a lot of stress over time throughout our legs, hips and lower back. It also decreases running efficiency, making us work harder for the same pace and distance. This can often combine with slower stride frequency, which adds to the inefficiency.
Although here is a one thing to note: barefoot running actually takes slightly more work because it is using the foot muscles more. However, this insight can be balanced against the extra energy it takes to run with overstriding versus the gait changes for barefoot running.
Here is what one study had to say on the gait changes for barefoot runners:
"overall less maximum vertical ground reaction forces, less extension moment and power absorption at the knee, less foot and ankle dorsiflexion at ground contact, less ground contact time, shorter stride length, increased stride frequency, and increased knee flexion at ground contact"
The above summarizes the greater amount of work required to run barefoot. Barefoot runners also tend to land on the balls or midsole of their feet, which also requires the calves to work harder. This is sprinting form, which has a different set of requirements than distance running. It also gives less opportunity for the body's natural flow of storing and releasing tension (which is stored energy) through tendons and a larger array of muscles.
So what should we do then? Barefoot running hasn't been shown to provide any benefits, and yet running with well cushioned shoes also leads to injury.
My answer is this: run with cushioned shoes but learn how to run safely at the same time. Just like one wouldn't expect to be effective at sports like tennis without learning the form and technique, don't expect to be able to go running effectively and safely without getting some professional help.