I am working on proofreading a first-time novel. The author repeteadly uses 'said' as part of a kind of compound verb (dropping the subject after 'and'):
"I don't understand," he said, and then walked away.
"This is your fault," she said, and turned to face the mountain.
"I'm sorry," said Bill, and smiled.
As much as I feel sure that this can't be right, and that the compound verb is broken by the unconventional syntax around 'say', I can't find any grammar rules or explanations to help clarify it. Of course, just adding another subject before the second verb would fix it, but I'd like to know how to explain that this more concise structure is wrong.
Am I right and this is wrong, and why?