I must have a clear purse to carry my diabetic supplies at work. The problem? After a while, the corners develop holes which are small enough to not really matter, but they scratch my skin and hurt.
You can try pushing in the jagged edges and putting on a clear epoxy from the inside to keep them shut.
"Plastics" actually come in many different forms so be careful and give your repair ideas a lot of thought as what may work okay on one type may not do well on another.
If you decide to use a tape I would suggest you try to file down any really sharp edges. Maybe try some sandpaper or a nail file might work. Edges should be pretty smooth or they may poke a hole in the tape after a period of time.
There are a few methods you can try to repair the corners of your bag.
Secure edges with duct tape or clear packing tape.