I am guessing that because bears have extremely sensitive smell, even if a bear understood footprints, they would not find this nearly as reliable as following their scent. But could it actually be that some predators, seeing footprints either follow or avoid the path? Could they even understand the direction a human had been walking in?
Generally they will avoid humans as much as possible, except for occasional animals that have become habituated to humans. This is especially so for animal species that have been hunted extensively at some point - those that could evade humans survived and passed on their survival instincts!
In response to a comment from @LorenPechtel: survival instincts in this context could be either taught or genetic. Many species will teach their young to avoid certain things rather than leaving it to genetics to determine what is dangerous and what is not. However, there are certain avoidance behaviours to objects that seem to be genetically inherited that I would have thought could only be taught. Such as a fear of snakes in captive monkeys that have never seen snakes before.
Generally they can tell direction of travel and approximately how long ago based on the size of scent trail and strength of the smell. If you have ever observed a search-and-rescue dog working, you will find that once they are locked on the target, then tend to zig-zag across the scent trail, smelling for where the edges are and travelling in the direction of the stronger scent. This zig-zag will get smaller as they travel towards the object because of the way smells disperse in the air in a cone shape, with the pointy bit where the object of interest is.
For most common predators, I doubt that they will use their eyes for this. AFAIK we have no way of telling what an animal thinks based on seeing tracks, though many animals are capable of recognizing objects visually. Any sort of recognition (visual, scent, sound) would require some familiarity with the object of interest/avoidance, though unfamiliar objects often cause an aversion in many wild animals (fear of unknown).