I have noticed that when driving at night (or whenever I have the headlights on), when the fans turn on, the lights dim for a split second, and the engine kind of skips a beat. The lights dimming is like the opposite of somebody flashing their high beams. The headlights, including the dash lights, dim for about a quarter of a second (very rough guess). I'm not sure if the engine skipping is actually a misfire or not. It's like somebody took their foot off the accelerator and put it back on really quickly. The revs drop, and then suddenly rise again. You can barely feel it at higher rev ranges (2500 - 3000rpm), but at lower speeds it's much more noticeable. Turning off the stereo and air conditioner doesn't do anything. I haven't noticed the misfire doesn't seem to occur when driving without the lights on, but that could be because the majority of my driving is at highway speeds. I have also noticed that the fans turn on and off fairly often. Even when travelling at 100, the engine is fairly cool (stays about 1/6th of the way up the gauge), but the fans are turning on every 2 or 3 minutes.

I also noticed today when idling for about 5 minutes, my driver side window wouldn't wind up (power windows), but it would go further down. All the others worked fine, and as I drove down the road about 50m, it would wind up very slowly. Then, after another 50m or so, it was working fine. Could these issues be caused by something like a battery starting to wear out, or having the wrong type? The little indicator on the battery is still green.

I think you might have a prob with the charging circuit.
As in a resistance somewhere.
That could mean loose connections , slipping alt belt or something along those lines.

sounds like a bad earth! Poor connection on the battery or an earth strap broken!

Check alternator output - read voltage with hot engine idling and headlights on full. Should be 14.2 volts or thereabouts.