Here are some other suggestions. It's a fairly long list, but I'm not suggesting we'd answer every question for every book... just pick the ones that make the most sense for that book.
Words
Is the book intended for a child to read to themselves or for an adult to read?
What are the most difficult words used? Does it use contractions?
Does it used advanced structures like similes, metaphors, etc?
Does the book contain dialogue? How is it structured?
Plot
Did the author use repetition / how did the author use repetition?
How does the story problem escalate?
How is the story resolved? Is this resolution satisfying?
How well can a child relate to the situation?
Character
Who is the main character? (Name, age, race, species, sex, gender, etc.)
What makes the main character interesting for children?
Who are the main character's family and friends? What roles do they take in the story?
Setting
Where does the story take place?
How long does the story last? (A day, a few hours, etc)
Art
What style of artwork was used? (Cartoony, realistic, surreal, highly detailed, minimalist...)
Does the art enchance the feel of the writing?
Is the picture book's main appeal the writing, the words or both?
Does the book employ the other senses? (Pop-ups, textures, noises, etc.)
Overall
Did you enjoy the book? Would you read more by this author?
Is it the sort of book you / a child would re-read?