I too initally had issues when I plugged some external speakers into the jack to play a Netflix movie. No sound. And then I tried some headphones and still no sound. Then tried an expensive pair of canal headphones and it played only after using force to seat the plug.
Not all 3.5 mm male connectors are the same. Some are of different lengths but hard to notice unless you hold them next to each other. Luckily my problem was I did not to try and jam the first two plugs I tried out deep enough as I did not want to damage the connector inside. The jack on the Charge is definitely a tight fight. I had to really push hard until the jack finally seated and it started playing.
But I'd rather it be a tight fit over a loose one. Tight will loosen over time anyway.
You shouldn't have to jiggle it though to get it to play. Just cause you exchanged it doesn't mean you didn't get the same possible poor assembly issue if your replacement came from the same lot at the the same store!
Try some other headphones out in a store to isolate the issue of jacks of varying brands. Over the years, I find some jacks collars are in different places which varies how deep a jack goes even though it's still 3.5 mm in diameter. Some have a different tip styles too which can affects a connection.
If all else fails, have them exchange it again, but bring in your headphones with you, so they can try your current Charge out with your headphones to rule out a bad male jack end.
I have not read of many jack issues on any Charge forums other than the known issue that when using an HDMI cable, it does not give us an option of allowing us to split the audio signal through the 3.5mm jack to pass the audion to a stereo system or external speakers. Hopefully they can address this in a next software update.