Sam,
I've thought of one possible assembly error that would cause both symptoms: Take the magazine out and shine a flashlight up into the magazine well. If you see a flat spring finger sticking out into it, that's the culprit. The last person to assemble the gun got the middle flat spring finger under the disconnector rather than over it. This does three things:
1. It makes the left spring finger, intended only to push the sear under the hammer hooks on cocking also do the work of pushing the trigger back forward. Normally both it and the middle spring finger (working through the disconnector) do this job, and that will make the trigger pull light.
2. When a magazine is in place, this leaf prevents the trigger from returning to full-forward position, and thus the grip safety hand never slips off the top of the trigger bow to pop in behind it to block trigger operation.
3. (AND THIS IS DANGEROUS) Without the middle spring finger bearing against its back slope, the disconnector isn't working and the gun can go full auto. It might not, depending how you grip it and whether that long slide moves forward fast enough to let the hammer drop with ignition force, but if you have ever noticed the gun failing to cock the hammer when it cycles, this assembly error I described is pretty certainly the cause.
Either of the other two answers posted may also be correct. If you don't see the spring finger sticking into the magazine well, tip the muzzle up and down to see if the grip safety moves? If the flat spring is tensioned correctly, the grip safety shouldn't move under its own weight. You should also be able to depress the bottom end of it and see it spring back.
Next, grasp the sides of the trigger and try to pull it forward. If the middle finger of the leaf spring is correctly set, the trigger should already be as far forward as it can go. If you are able to pull it forward, see if the grip safety pops a little further out when you do? If so, failure of the trigger to go fully forward is trapping the grip safety hand (as I described in 2., above). In addition to my assembly error speculation, this could also happen either if the flat spring fingers are simply incorrectly tensioned or if a match trigger has been fitted incorrectly. In the latter case the trigger could either be dragging in its frame channel, or the back of the trigger bow could be bent outward, effectively making the trigger too long for the grip safety to work.
If you none of this tells you anything and you are uncomfortable doing full disassembly, send the gun to the factory with a note explaining the problem. If the gun was sold as new and you never disassembled it, they will almost certainly correct it for free. I believe you can still send a gun directly to the manufacturer and he can send it directly back to you all without going through an FFL holder. This apparent exception to the FFL requirement exists both because ownership isn't being transferred and because nobody wants to discourage owners from making their guns safe. But call Springfield Armory just to be sure. Some states might have exceptions.
The advantage to factory return is you get some special attention given to the gun by those most familiar with it. I have done this twice in the past, once with a Charter Arms Bulldog, and once with a Ruger Redhawk. In both cases my complaint was poor accuracy. In both cases they came back shooting exceptionally for their class. The 3" Bulldog went from printing 7" groups 5" low and left at 25 yards to shooting 1.5" groups about an inch high and left at that same distance. The Ruger went from delivering 4" groups at 25 yards to pasting 1.25" groups at 50 yards (scope sight) with plain Jane American Eagle 240 grain rounds. The factories recognize the importance of their word-of-mouth reputation among customers who know enough to care, and they have people ready and able to make them happy.
Nick