I am working with a 3-way switch that has two can lights. I replaced one can light with a small 5-bulb chandileer and was unpleasantly surprised to find the bulbs only partially lit. There is another can light on the 3-way switch system that works properly. There wasn't a red wire on the line so I am not sure how they got the 3-way switch to work. Anyway, I took the light down and attached a plug to it and wouldn't you know, it worked fine plugged into the wall. I don't think I messed up the wiring so I was wondering what would make the bulbs so dim?

Bet this is going to be a devil to track down.

It sounds like somewhere in the circuit that the hot is run in series through a fixture - instead of the fixture tapping into the hot and neutral. While the first fixture will work, any down stream would be using power fed through a light bulb filament - causing a power drop and dim lights.

If you can get to the wiring on that can that does work you may find your problem there. However, if your three-ways are wired strangely as you indicate, no telling where the problem will actually be.

any resistor connected in series will show a voltage drop, a simple voltage detector should identify where the potential drop starts.

"There wasn't a red wire on the line so I am not sure how they got the 3-way switch to work."

Umm, it's a 3 way switch, what was connected.