Set your multimeter to the lowest resistance setting, mine is set on 200 ohms. Use the leads to probe the board and verify trails that should be connected show near 0 resistance and trails that should not be connected show infinite resistance.
Non Connected Trails
If you have a gap in a copper trail, you can solder over the trail to ensure a good connection. If you have two trails that are connected and should not be, use a dremel rotary tool to remove the copper connecting the trails. If a trails is damaged beyond repair, use a dremel rotary tool to remove the trail and replace it with a normal insulated wire.