Delightful Reading’s lesson plans include an informal introduction to spelling. Every time a new word is introduced, the child is encouraged to look at it closely, then try to spell it using his letter tiles. You could do the same thing with your 3rd grader’s copywork. Give him a short assignment (a line or a sentence to begin with) and tell him to look closely at the words’ spellings as he is copying them because you will ask him to spell one or two when he is finished. When you give him the word(s), he can spell them using letter tiles or verbally or whatever.
It sounds like he is reading so quickly that he is not looking at how the words are spelled. This little exercise will encourage him to slow down enough to pay attention to spellings as he reads, which will be a great preparation for dictation next year and the rest of his life.