I am sure this is an all too common part, but since I am new to this hobby,
I have no Idea what it is.
It looks like a glass or plastic capacitor or resistor, maybe neither,
with copper windings inside, and it has a small crack running along the bottom.
I just replaced most of the capacitors, should I worry about this?
Also, the light blue rectangular resistor next to it looks worn, should I replace it, or do they commonly look that way.
Thanks for any help!

Magnavox300

I don't think there's a problem with either component. The clear item is a peaking coil. If there's a continuity reading, it's a strong possibility it's good.

Yes it's an inductor and should measure a low resistance. The white item is a capacitor, if I am correct to which part you refer, and it looks fine. If you are worried, disconnect one end and measure it. It's marked with capacitance, 0.1 microfarads.

Both probably fine. The resistor is just a bit grungy, no worries. If you're worried about the cracks on the coil, a little service cement would seal them up so no moisture get's in and causes corrosion..

Thanks for all the excellent responses,
good to know what a peaking coil is!
I wonder, are they made of glass or plastic?

Magnavox300

A peaking coil, at least this one, is likely made of insulated copper wire wound on a cardboard tube, sometimes with a magnetic core. Copper wires soldered on the ends and the whole thing impregnated in some kind of plastic goop.

Thanks!