Is the following sentence correct? The two verbs do not match.
I saw him leave the house.
Can we rephrase it to "I saw him leaving the house."? What is the difference?
It's not a matter of 'matching'. We can see someone do or doing something. The infinitive suggests that we see the whole action, the gerund that we see it in progress. With a comparatively short action such as 'leave the house', there may not be a significant difference.