If you mount components on the copper side, you should cover the long leads with insulation to prevent them from short circuiting on the tracks.
I don't see what's so hard about mounting them on the non-copper side. I don't even bother planning all of the connections. I just roughly lay out the board, so the components are roughly the same place as is on the schematic (looking at it from the board side), tack them into place (just solder enough of the leads to secure them the right place), solder the links (ticking off each connection on the schematic as I go), check the board, completely solder the components and check again before cutting the unneeded tracks. Before applying the power, I give the board a final check over, looking carefully for solder bridges, dry joints and checking against the schematic again.
In short I disagree with putting all the components on the copper side. I think the risks of it blowing up outweigh the perceived benefits of saving time (I'd question that too, I don't see how it's any quicker). What's better for you to spend a little bit longer and it work first time or it blowing up and you have to replace lots of expensive components?
There's nothing wrong with mounting the odd component on the copper side, but it should only be done when the non-copper side is already full and there isn't space for it.
I don't use much stripboard nowadays, I breadboard it and make proper PCB, once I'm happy with it.
I'd also question whether the traces on the stripboard are thick enough to carry 3A, without overheating.