I've never used a barrel jack connector, so I was wondering if I should put some kind of liquid tape or insulation around the soldered connection from the wire to the barrel jack? By wire to barrel jack, I'm referring to the end of the barrel jack to the microcontroller.
You can use [u]heat shrink tubing[/u] over the whole thing, and ideally smaller heat shrink over the soldered connections. The heat shrink will work better if you remove the nut & washer.
Electrical tape (or any kind of tape) can be used as a temporary solution.
That connector is intended to be mounted in a panel with the solder joints inside an enclosure so it doesn't need to be protected but we have some heat-shrunk connectors like that for "burn in purposes".
And yes, polarity matters with DC! Do you have a multimeter to check the polarity?