There's no in-universe reason provided but there are rumours that it was done in the mini-series because SciFi was constantly pushing them to "cut corners" in addition to providing a neat styling difference. As an in-joke they did exactly that on all the paper in the show. However there's alternating versions out there, as highlighted in this quote from Wired:
Wired.com: Did it have anything to do with cutting all the corners off
Di Justo: [Laughs] To the best of my knowledge, no. I think that was
just a joke about having to cut corners on the show.
[Editor's note: In a press conference at the Science Fiction Museum in
Seattle, executive producer Ronald Moore said that this story was a
myth. "These people just hate right angles," he said.]
To expand on the Editor's Note, there's this obviously tongue in cheek quote:
1/30/2005 -- Question: Why is it that the paper in the Galactica
universe has the corners cut off, even the tractor feed.
This is a closely guarded secret of the show and certainly not a wacky
design element that someone came up with during the miniseries.
The producers have since commented that it became a massive nuisance once the show was adapted to a weekly television series, because it became quite a bit of work to repeatedly remove the corners.
What do the humans in the show have against right angles on paper
Moore: Now that's one of the deepest mysteries of the entire show.
That is the Da Vinci Code of Battlestar Galactica.
Eick: That's purposely left unsolved just to torture the fans. All I
know is the prop guy from the miniseries who had that idea lived in
infamy for the next five years, with assistants shaving corners off of
everything in sight, saying "I want to strangle whoever had this
Over all it sounds like a deliberate design decision, something simple but obvious to indicate the small differences between Battlestar's universe and our own but there may well be some truth to the original rumour, i.e. whoever originally came up with the idea may have been inspired by the cutting of corners in the miniseries.