Keep an eye on the fish to see if they're nipping each other, or if they are catching their fins on the sharp points of decor.
If they're just small tears, they should heal quickly. If the animals are sick, they won't heal quickly. Some long fined variety of tetras, like black skirts (widow), white skirts, or serpae have a natural "frayed" look to their finnage, especially the serpae.
If you are very worried, try using Melafix medication. It's an antibacterial that should help prevent infection of frayed fins. If they don't heal in three to four days, and it looks as if the fin is getting shorter, you may have to move up to a stronger medication because you may now have parasitic fin-rot in your tank, which could've been brought on by stress of cycling.
~~Colesea