I got a Veil Tail betta about a little over a month ago in a one gallon Aqueon Mini Bow. (I'm working on getting something at least 2.5G, but for now...) I have a mini heater as well.
After two weeks or so, I noticed his fins were getting a bit tattered, and then one day it just looked extra extra tattered and after reading up on here, it looked like I should take out the filter and be super diligent with water changes. So I did that for about 2 weeks, but realized that the water wasn't getting heated up. Because there was no circulation, my crappy little heater was only heating the little bit of water around it. But Fredrick (my fish) wasn't ever hovering near it or anything and was eating and swimming around mostly (less erratically too). The water was between 60-70. His fins were looking like they were healing a bit too. But about two days ago when I tried to feed him he didn't come around all excited and didn't even try to eat the food! And I noticed he was significantly paler and I thought I could almost see stress stripes.
I remembered then that I had read somewhere that sometimes bettas like the filter water flows, but will end up with tattered fins. As long as the water is kept clean to prevent infection, it is okay. So I put the filter back in (with a new cartridge) and the water is back to 75-85 and his color is all back... BUT his fins are super tattered already and his anal fin has split in half like two fins, one of his ventral fins has has a white tip now. (I am still looking for my cord to get pics from my camera to my computer)
Anyway, do you guys think the tattered fins are okay in this situation? His color is beautiful and he eats and gets very excited for food time. He'll flare if I put the mirror up, but I avoid doing that because I feel like it's bad for his tattered fins. He made a bubble nest when I had the filter in, before I had tested seeing what it was like with the filter out. I just want to know what's best for him until I can get him a larger home... Without the filter, it looked like his tails were slowly healing, but the water was so cold and he got pale and didn't eat... With the filter, I think he seems fine (he's also my first betta), but his tail gets super tattered.