A plant still produces a net positive of oxygen though, correct?

Sort of, a plant converts a net positive of CO_2 to O_2.

This is also another one of those cases where some folks can misunderstand the statement to believe that plants somehow take in all this CO_2 and scrub it of Carbon. Not really, that Carbon becomes the plant itself. The amount of C's that a plant pulls out of the CO_2's is nearly equivalent to the plant's dead weight. This is important to understand, because old growth forests don't actually remove net CO_2 from the atmosphere, they just fail to release it. If you cut down the forest, the dead plant matter starts decomposing and/or burning and then CO_2 and/or methane goes back into the atmosphere.

Or at least, that's how I understand it.

Essentially correct. There may be some second order effects that help established forests pick up some more carbon out of the atmosphere, especially if the atmosphere gets more carbon laden than it used to be when the forest was formed. The Economist had a special report on forests last week that had some details on the climate benefits of old forests.

Only during the day from what I've read. At night they consume a net amount of oxygen.

The amount consumed is smaller than the amount produced, so there is a net production over the whole cycle.