I have heard that there are certain electronic items that are not permitted upon entry into China. Does anyone know if portable DVD players are allowed in?

There should be no problem.

I'm not aware of restrictions on electronics. Journalists have to register their items, I assume you are not a journalists. You can't bring in the DVD player for sale to someone in the PRC, only for your personal use while there and you have to bring it back out with you (same as in any other country). Other than that, there aren't any restrictions that I am aware of. You can't have any DVDs which are "detrimental to Chinese national security", i.e. I wouldn't have the player loaded with a DVD about the Dali Lama, free Tibet or independence for Taiwan.....

How would they know if you didn't bring it back with you? You don't have to register it when you enter China.

Not an issue. If you had broadcast style video cameras, that would probably cause a stir.