Why do my new door hinges prevent my door from shutting completely?
How do I go about fixing this? I guess I could take them off again, and chisel away a little on the door grooves or in the frame,


That's pretty much the only way - but take a good look and work out which side (door or frame) needs to move and in which direction. I've done this in the past and gone the wrong way at first which isn't good.

In some cases I've even had to resort to shaving a bit from the edge of the frame:



This shows the hinge side, but the same applies if the problem is occurring on the handle side. You only need to shave that part of the frame where the door and frame interfere. This might be the only solution if the door is warped or twisted at all as moving the entire door by repositioning the hinges would leave gaps between the door and the frame.