AH the good old LA 15.
Check all of the head and carb and back plate screws as they can be a little loose when new( true for all glow engines). I have seen some fuel leak around a loose glow plug as well. However some fuel can blow out of the carb at times such as a rich start or when running rich for break in and a little brown is fairly normal. Exhaust oil from the muffler joint is not uncommon either.
Have fun! Sealing the back plate with a little teflon plumbers tape won't hurt it any.