The coil simply turns primary ignition voltage into a vary high output secondary voltage.
Take a light tester and ground the clamp of the tester. Run the lead along the coil wire from the coil to the distributor.
While you are at it run the lead along each and every spark plug wire. If the tester lights up then you are experiencing a bad wire, bad spark plug, bad connection.
Take a can of carbuerator cleaner or brake cleaner and spray the ballaster resistors and the contacts clean. Oil, grime and contamination can cause problems in a weak primary ignition being sent to the coil. disconnect them one at a time, clean and reinstall.
If you have a vacuum advance on the distributor then chances are the mechanic didn't fasten the vacuum line securely. Check it. Check the other end and where it goes. On some there is a T fitting so check both ends.

An answer to your post
Here is a simple check you can conduct to determine whether your coil connected correctly negative polarity.
Take a spare spark plug and disconnect A spark plug wire. connect the spark plug and make sure the threads of the plug are grounded.
Start and run the vehicle. Take a pencil and insert it in the gap with the engine running and watch where the flare goes. If it goes toward the plug then the polarity is correct. High tension polarity if wrong will direct the spark the wrong way. It should travel from the L shape of the plug and into the electrode. If the pencil test flares toward the plug then good. If not then change the + and - on the coil.
I have heard mechanics state it doesn't matter how the coil is hooked up whether the lead from the ballister resistor contacts the positive or the negative and vice versa with the distributor. Wrong
The center of the spark plug is the hottest part of the plug and current should ground in that direction. Why? it saves current and as an end result it saves ignition components.