For an INSTANT EXPLOSION:
Hold down the Z button until the driver yells "Doh!" then a half second later the building will blow up. (works best with backlash)
Some people say the Z button trick is useless in Blast Corps. Certain levels are made very easy by the proper application of this trick, making platinum times a cinch! Get a really fast time on Oyster Harbor using a combination of tricks. First, it is not necessary to have the boats in place or fill the holes in order to complete the level. Second, it is possible to destroy the series of walls that one usually uses the TNT on, as well as the final building, using the Z button trick. So by destroying the small blocks in the beginning of the course using the Ramdozer, and using the Z button trick on the buildings, one can do the level in under 1:30, where the platinum time is 2:55!
Another hugely useful application of the Z button trick is on Beeton Tracks. Normally, one would have to move the Ramdozer across the tracks and use the TNT to blow up the big building. Instead, the Z button trick can blow it up, resulting in a time of around 33 seconds, instead of the platinum time of 1:15!
A somewhat less useful application of the Z button trick is on the last huge building on Diamond Sands. Most of it is destroyed by TNT, but the remaining part of the building can be destroyed without using the TNT on the other side of the tracks. Just use the magic Z button!
There are a few other useful application of this trick, but none as useful as the first two. It seems that the only win condition for each level is that no buildings be blocking the carrier. Everything else can be ignored, even if green arrows are pointing to it. Using this strategy, some levels have extremely easy platinum times. These tricks are most helpful when you get to the later levels, like in the Platinum levels.
Thanks to Revolution readers JJ Zoch and Dan Abbe!