I pulled my oldest out of public school, but my second child is still there until the end of this year. Yes, I did supplement, and if they every go back to public school I would certainly supplement.
The biggest areas of neglect at our school were in math (curriculum was about a grade level behind), reading aloud (we checked out our own reading books from the library and I asked some comprehension questions to test how much they absorbed), history, and geography. When my son was in school all day, he didn't have much energy for a lot of extra work with me, so I had to limit it. However, the summer is a great time to add or supplement subjects that you think are not covered well in public school.
An easy book to use is "What Your Kindergartener/First Grader/Second Grader/etc. Needs to Know" by E.D. Hirsch. It takes about 15 minutes per day to cover the book over the school year (according to the author).
I'm not sure if that answers your question, but hope it helps.