Use a rubric--- as others have suggested. That way as you're observing their project you can check exactly what they did or did not do. I also leave space to add in comments of my own and extra questions I have for the student.
My school's copier allows us to scan in papers and it'll email us a pdf of the copy too. I keep all of my graded rubrics on my computer and its something I can send off to parents should they complain.
Stand your ground--- you are the teacher and you're assessing the student. It's not the end of the world. You are NOT assessing the parent, so what the parent thinks the kid should have gotten is nonsense.
Also, NEVER NEVER NEVER share with a parent that you don't remember their child's project. It comes off as "I don't care enough about your child's work to remember it". And that REALLY upsets them.
Take this as a lesson learned

Not a biggie.