Heavy Static in the Radio
If the condenser is not able to hold a charge, there will be significant sparking inside the ignition system. The electric charge and the magnetic interference that it creates will cause a significant amount of static in your radio. Stations that you can normally here clearly will now be very difficult to make out and will cut in and out sharply. Since the sparking only happens when the engine is turned on, the radio will work normally when the engine is off and only the battery is functioning. Once the car starts again, the static will resume.
If you suspect the condenser is going bad, you can sometimes tell by watching the engine run while it is in idle. The point cover needs to be removed and some engines won't run without it, but if the condenser is going bad, you are likely to see a large yellow spark jump between the two contact points. A good condenser minimizes this to a small blue spark but the points are sparking full-force with a yellow spark if the condenser is failing.
If the condenser has been failing for a while, the contact points could be damaged from excessive sparking and it can become more difficult to get the car started and it won't run as smoothly. It may run smoother when the engine timing is advanced but will stutter when the timing is slowed down. While there are a number of different issues that could cause trouble starting the engine, when this happens in conjunction with the radio static and the engine sparking, the condenser likely needs to be replaced.