Mukkapazza has just posted a very helpful explanation under "Guardiamogli in casa!". I have re-posted it here for convenience:
Great brainstorming! A direct object pronoun directly receives the action of the verb. It answers whom/chi or what/cosa. Cosa mangi? Mangio il pane. Lo mangio. Chi ami? Amo te. Ti amo. An indirect object pronoun indirectly receives the action ;) and answers to whom/a chi? Chi piace a Marco? La ragazza piace a Marco. Lei gli piace. A chi scrivi? Scrivo a mia madre. Le scrivo. There are two pieces of good news. 1) the difference between IOP and DOP is only third person, and 2) often you can figure out which is which by doing an a preposition check: Le scrivo una lettera / Scrivo una lettera a lei / IOP In this case in particular you'll notice that Let's watch him! / DOP / Guardiamolo! So if gli means the action is being indirectly received, what does that mean? There isn't really an equivalent of this in English, but in Italian you could also say Guardiamo dentro casa sua! Guardiamo dentro la sua casa! Here are a few more to help clarify: Guardiamogli negli occhi / Let's look in his eyes Guardiamogli nelle tasche / Let's look in his pockets Guardiamogli la ferita / Let's look at his wound Hope this was somewhat useful. In the meantime, we'll work on making more helpful exercises for all of you :)
A similar sentence construction is used with body parts -e.g. "mi lavo le mani", where the possessive adjective is omitted. However that is a reflexive construction. See this link (scroll down to body parts): http://italian.about.com/od/grammar/a/italian-possessive-adjectives.htm I haven't noticed the above type of construction, but I will take note and ask my teacher!
Yes, but it might be a similar example of where you can omit the possessive. I am a bit sceptical myself. I found examples on google of "guardiamogli in bocca", "guardiamole negli occhi", and "guardiamogli dentro la lista" (let's look for him on the list, which is different to the forms here), but no examples like "guardiamogli dentro il computer" and "guardiamogli in casa" in this lesson (translated as "let's look inside his computer/ house"). It would be good if the language experts would comment.