Hola Ελισάβετ

Yes, this is using "le" as a direct object pronoun, instead of "lo" -both of them are correct because the Spanish Royal Academy accepts "le" with transitive verbs when it is referring to a masculine singular person (he). It doesn't accept the plural "les" though. We have a small champter dedicated to "leísmo". 

The difference between mirar and ver, I think, is the same difference between to look at and to see; mirar is used when we fix our eyes on something and pay attention to it. (this is the case in our sentence in the writing exercise), while ver refers more to the perception of things through our sight, it is more technical. 

Having said that, there are certain sentences that we use with "ver" that, following what I just said, would be more appropriate with "mirar", but we generally use "ver" (although it varies a bit depending on the Spanish speaking country):

Bearing in mind that watching the telly is something where we keep looking in on direction with full attention, it would make sense to use mirar instead, but we don't!!

Inma