Are your headphones plugged all the way in? Push harder then you think is necessary.

I had a terrible time with my iPod headphones or speakers working properly, I went to Apple HELP and was told to push the plug in til it touches the device. works perfectly now.

Good luck.

That is definitely not a normal situation, if you are pushing it in till it clicks in fully plugged then you have a problem in the device, try the plug again, then contact the company and tell them what is happening, they should send you a new one.
On all of mine when the ear buds are in the sound only comes from them, removing them should not affect the play of the video, have you posted about this on the nexus forum, if not do so to see if this is happening on others. It could be a bug that affects all of them.

Maddielee, you were right--I didn't have the plug pushed in far enough. But the videos and music tracks still stop when I disengage the plug. And the sound coming from the tablet speaker(s) is weak and tinny. I'm wondering if the speaker is blown. I found the following on Geek.com:

In some cases, the Nexus 7 has quickly blown a speaker or has had a blown speaker on arrival. Anyone who knows what a blown speaker sounds like will recognize the problem immediately, and it will not be difficult at all to demonstrate this issue to the customer support if this problem occurs for you.

I'll check on the Nexus forum. Thanks!

I would say that is probably the problem and if it is happening this frequently already that is not good.

I also recently read that Google has said that the usb port absolutely cannot be used to attach a thumb drive or external hard drive to the nexus, it can be used to attach a mouse or keyboard only. This is very bad news, it was one way to get around the lack of SD card slot, really disappointed in this. The lack of SD support is just baffling since the majority of tablets have it.

It sounds like you probably should contact them soon about this speaker issue.

Meanwhile, my son came by and said my speaker doesn't sound blown at all. In fact, it sounds good considering it's coming from a device that's only a half-inch wide. He also thinks the pause when you insert the jack and the stop when you disengage it is intentional--a desirable feature. He may be right; I'll have to read further in the guidebook.

Yes, I'm sure a lot of people are disappointed in the card slot situation. Odd that they didn't address this in the design.

Wil have to try the sound. Frankly, I bought mine mainly for book reading. I don't expect to listen to music with it. Not a big game player either although I put a couple of simple games on it.

I just read today that Asus will be releasing their own version of the nexus and it will have the Sd card slot and a few other things. I guess they didn't want to let Google have all the good stuff. Will be interesting to see them compared.
I also read that flash can be loaded and work on the nexus, some people on a forum were talking about side loading it.