The Marlin "trigger flop" is well known. It came about when Marlin introduced the 2-piece triggers to keep their lawyers happy (which is why tommyv's 50 year old rifles don't have floppy triggers).
While annoying, it's nothing to worry about: the rifle is perfectly safe.
If it bugs you enough to spend money and a little time to remove the flop and get a better trigger, order one of Wild West Guns' "Trigger Happy" kits from Brownells, Midway, WWG, etc. Costs about $90 and takes 10 -15 minutes to do.