I must take some issue with your analysis of “See Spot run”. The object of the verb see is ‘Spot run’, not ‘Spot’. Had I wanted to say “See Spot,” I could have said just that. “Spot run’ is a clause, the object of the verb ‘see’; it consists of the infinitive, ‘run’ and its subject, ‘Spot’. You might ask why the verb isn’t inflected to agree with the subject, and the answer is that it isn’t a verb – it’s a verbal noun i.e., a word which is a noun, but being formed from a verb may still take a subject and an object. We might get some clues if we investigate another language; granted that language has a grammar all its own, which is different from that of English, but still, we might get some hints. In Spanish consider the sentence, “Quiero correr” (I want to run); we translate ‘correr’ as the infinitive ‘to run’. But in “Veo el niño correr” (I see the boy run), we translate this obvious infinitive as either (the infinitive) ‘run’ or the gerund ‘running’, and while boy is the obvious subject, the verb[al noun] is never inflected, and never translated as ‘to run’.
LINK TO COLUMN: How do you diagram the sentence, “See Spot run”? - The Straight Dope