I wish I could count the number of rifles I've seen built this way, usually with the trigger plate inlet too deep so that the trigger bar pushes against the sear when unset. Almost always the builder insists that it works correctly!
Assuming it's not fixable with the screw adjustment, if the plate is set too deep, the fix may be as easy as shimming it a bit so that the bar doesn't ride on the sear. If not, you might have to take material off the trigger bar or (last resort) bend the sear up a bit.
I don't like to leave setups like this, because it is possible for the cock to slip if you try to pull it back to half cock without setting the trigger.
Just my 2¢.