http://www.dartmouth.edu/~german/Grammatik/Nouns/accusative.html (bottom of the page)
Don't take this one too serious.
That doesn't stop the "Rolling Stones" from singing:
"A smile relieves a heart that grieves, remember what I said. I'm not waiting on a lady, I'm just waiting on a friend. I'm just waiting on a friend, just waiting on a friend. I'm just waiting on a friend, I'm just waiting on a friend, just waiting on a friend."
"warten auf" only means "wait on" in the sense of "wait for", not in the sense of serving people in a restaurant.
It really depends on where you are, at least in the US I think it is regional. For me (grew up in the Chicago area) I use "wait on" in both cases for "wait on - being served" and "wait for someone/something". But to my wife who grew up 2.5 hours south of me "wait on" is for being served only.
For this English speaker (northeastern US), "wait for" and "wait on" have slightly different meanings. Wait on has a subtext that everything is ready but you are waiting on someone/something. Think the car is packed with the family and ready to leave on vacation but the father is still doing stuff inside "we're waiting on your father". Or three meals have arrived for a table of four at a restaurant. The server who is "waiting on" the table may say "we're still waiting on the last entree". In both these cases "wait for" could be used, but "wait on" says this specific thing is holding up the process.
"Wir warten auf ihn." has only two possible English translations no matter what the context will be.
We are waiting for him.
We are waiting on him. (second version more likely used in: We are waiting on a friend.)
If watching for is given as an option, -it is wrong!
For those wondering why the preposition "auf" -
Some German verbs take set prepositions.
Verb / Preposition / English / Case
mögen / an / to like about / Dative
sprechen / mit / to speak, talk with / Dative
sprechen / über /to speak,talk about/ Accus
denken / an / to think of,about / Accusative
antworten / auf / to reply to / Accusative
hören / auf / to listen to / Accusative
warten / auf / to wait for / Accusative