Looks like he either got snagged on a filter or decoration or he's nipping his fins.
Go over your decorations with a stocking. If it snags, it'll rip fins.
If he's nipping his tail, make sure you have a set schedule for night and day that you don't stray too far from. Make sure he's got things to hid behind/in and explore as well as time to exercise any excess energy.
A hand held mirror is a good tool to get some exercise and boost self confidence. Make winning easy at first, but slowly work them up to a minute or two of flaring before taking the mirror away.
Plastic bottle caps are also a good source of entertainment. You can use different colors to see which your betta prefers.