Is wearing a shirt mandatory?

For boys or for girls? :-P

During the pre-race meeting at the last tri I did, they specifically said "No nipples for the bike and run!"

USAT tried to make a rule out of that a few years ago.  Didn't fly and they dropped it.  But as mentioned, it is at the race directors choosing.

Yep, what he said. For example, WTC races, like the branded Ironman and IM70.3 races, use modified USAT rules that do prohibit naked torsos on the bike and run.

In Canada is is mandatory to wear a shirt but not in the US but like others say some Race Directors make it mandatory.

If it is not mandatory, is there any advantage to wearing a tri top?

I think one advantage is that on a bike since wind is constant hitting you, your body begins to cool down... I mean it feels nice but it might affect your performance? Don't take my word for it I am still new to all this.

There was no rule saying you had to wear a top in my HIM here in FL, but you had to wear a top in my last HIM in WA.   Allot of people don't wear tops around here for sprints and olys.  It all depends on the rules for that specific race.

Less road rash if you fly off the bike?

Better evaporative cooling with a top?

If it's a longer race you can throw some gels in your tri top...otherwise I'd say it's just aesthetic. 

Speaking of which: at the Timberman sprint there were two guys--larger gentlemen, I'd picture them sitting at a bar watching football before I'd ever think about them in a triathlon--wearing speedos, just speedos, with 'Team (something)' on their backside...I think I erased what it said from memory, it was not a pretty sight.