The "moving" contact breaker point has to be insulated from the pivot. They normally run in an insulated bush arrangement. It might be worth double checking that all the washers and bushes look to be present as that could be the source of your short to earth. However, if its a replaceable unit then that does seem unlikely. However, it will be worth checking that the LT wire is not damaged where it passes though the distributor body and that the insulating washers are present where the wire (and condenser lead) clamps to the contact breaker points (the current can short to earth via the spring otherwise). Condensers don't usually short out when they fail but you never know.....
Good luck!
Keith