Also: If re-potting is recommended, would this be a suitable pot?
http://www.noveltymfg.com/Products/SquarePlanters/EllaSquares/tabid/223/Default.aspx

It has "water-minder" feature that somehow collects water and re-feeds it to the plant automatically.

Here's the description from the website:

"ArtStone Planters have an intricate self-watering system that, in an indoor environment, refeeds water to the plant via its roots. The system has a bottom reservoir in which water accumulates and allows the plant to grab refreshment when needed.

The water-minder disk is glued to the bottom of the planter and secured by a peg in the middle, assuring a tight fit so the water feature does not free itself from the planter."

I'd repot it into a simple terracotta pot. Jades don't need a lot of water, and the "intricate self watering system" sounds like a good way to kill a jade. If the plant is wet right now, repot asap or make sure the soil is able to dry very soon.

Not only does it not need a lot of water, it needs us to be in control of when it's watered, not the pot's determination.

FYI: the plastic pot isn't all that problematic here, likely the soil is the real culprit; more appropriate soil could be OK in a plastic pot, if watered carefully.

Thanks for the replies. Here are the promised pictures (based on these, I'm rethinking what I said before about the plant being healthy...):

{{gwi:531478}}

{{gwi:531480}}

{{gwi:531482}}

{{gwi:531484}}

To me, the plant looks fine. The soil looks like it's water retentive, and I would change that if it was my plant. At the very least, make sure the soil is dry before watering again. Once Summer comes, gradually move your little guy outside into some good sun light. It will thank you.