I've only worked with sheers a few times. I press the hems/casings using a cloth and low heat so I don't melt them. I also pin to keep the hems in place and go slow, keeping the fabric taut to prevent slipping. I also use longer stitches, but not quite basting length stitches. HTH
Hopefully you'll here from the experts on this.

I always use a new needle for sheers, they can snag so easily. Second the suggestion to use lower heat on your iron. Also check the needle size, usually need a smaller needle for thin fabrics. Good luck!

It depends...I shortened sheers for the guest room and expected all kinds of trouble, but had none. Be sure, when you're sewing to hold the fabric in back of as well as in front of the needle and don't just push it along.

And lighten up your presser foot pressure.