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It might help weed out some terminally stupid people who post pictures of themselves destroying their apartment, but that's hardly a guarantee that it won't get damaged. Puke on carpets happens. People put holes in walls to hang things. This is all normal stuff that every landlord should expect to have to deal with and trying to find the perfect tenant that will result in zero maintenance is a waste of time.

For the pet issue, yeah if you don't uniformly enforce the rules you have, you're going to have a bad time. That should be common sense. If pets aren't allowed, then don't allow pets. That's pretty simple. There are plenty of places that might allow small pets but not a large sheepdog and that's perfectly fine as long as its clearly spelled out in the lease.