Making mistakes when reading aloud is common in young kids. My kids' elementary school principal had a little poster about it on her wall a few years ago. FWIW, I used to get very frustrated with myself in first grade for making mistakes when reading aloud.
I definitely wouldn't worry about turning "he is" into "he's". I agree with Lepa that he could be doing that deliberately. I do that; "he's" might sound more natural to him, and it's not changing the meaning.
I also agree that too much correcting could make the problem worse by stressing him.
