Can exercising with no shoes on be bad?

Yes: Injuries of many types may be more likely when exercising without shoes on.

Depends: Barefoot running something to consider. For many this is felt a means to lower injury rates by strengthening feet and returning to a more natural gait. For others this is just not the way to go due to previous injuries, foot alignment, running gait. If you decide to make the change to barefoot do so with caution- take is slow, consider minimal shoe first, run on soft surface, watch for obstacles.