If the drums were filled with AMFO then it'd produce a healthy explosion. (AMFO is what was used in the Oklahoma City Federal Building bombing back in the 90s, it's a mixture of fertilizer and fuel.)
Really, I don't think it matters much where the explosion comes from as I say something like that should fall under suspension of disbelief. Either it was in the guy or "somehow" The Joker had gotten explosives into the building. Hell, maybe the detonator caused the gas-lines of the building to ignite and explode (and yes, in the real world this wouldn't happen but movies often portray a gas leak and a spark as causing a huge explosion.)
It's much harder to try and to make sense of the large amount of explosives on the ferries. Given the tense situation in the city and the critical nature of needing to use the ferries you'd think it'd be ensured they were 100% free of explosives. But, I suppose, even that you have to wave away as suspension of disbelief.
For me, if the story itself is good enough I'm willing to ignore a lot
when it comes to things like this in movies.