Like, if you're holding a coffee on the ceiling, does it fall ten feet to the floor or just sit in the cup normally. Lots of little details to smooth out.
Sorry, but you've got more than little details to smooth out.
As soon as one way of movement can ignore some of the existing energy constraints (walking on walls ignores gravity), you have to take care, or you get perpetuum mobile, aka infinite energy, rearing its ugly head.
Make a high frame, one side of which is a slick metal wall. Take a big block of something heavy. Attach it to some railing on frame corners, so it is stable. Add some pulleys etc, and let it fall slowly to ground. That will generate you some energy in pulleys that you can easily convert to electricity. Then, instead of lifting it back, push it along the wall. Make the block be as slippery as possible to minimize friction. In fact, there are ways now, that claim to reduce friction to almost zero on macroscopic levels, but it even needn't be that bad. It is very possible to push even normal heavy loads across floor that you can't lift, showing that pushing uses way less energy than lifting.
Blam, you got energy. If energy of pushing < energy gained during fall, you get an energy surplus during fall = free energy. If you need human to push it, it might not be that bad. Otherwise you can just store that fall energy in a spring or something and make the push happen automatically. Probably will still get more energy out than you put in.
In fact, storing gravity energy is a thing, with a number of attempts currently in the world. And that is even without having the luxury of lifting the weight without gravity.
What happens in worlds with infinite energy is debateable. However, as soon as there is too much energy in something, it tends to explode. There are several questions here on WB about that.
As an afterthought, if people can walk on vertical surfaces, you gotta redesign security. Upper floor windows are now not safer than 1st floor. Mountain ranges are strolls in the park. What about cars? Do cars with peoiple in them can drive on walls too? There are tons of questions and on almost every aspect the world is very weird indeed.