Am I reading this right?

I can have a lightsaber that requires no advantage to crit?

Other modifications or talents that reduce advantage to crit specifically say "To a minimum of 1"

Jury Rigged however does not say this.

Wondering if this is a mistake, or if it is really intended to make zero crit rating weapons.

You cannot have a zero crit rating weapon. Jury Rigged should follow the rules of every other type of modification. Having something activate when you have no advantage brings serious questions that the system can't really answer such as: what if I roll threat? I don't need any advantage to activate this anymore, can I still activate it?

As a side note, I don't know if I'd allow Jury Rigged to work with Lightsabers. Not because of a power issue, but because they are already custom weapons, made by hand (or the Force or whatever).

Jury Rigged makes sense with mass-produced weapons, but Lightsabers are made by individuals, and I assume are already optimized.

It's a minimum of one (1).

"... decrease the Advantage cost on its Critical, or any single other effect by one to a minimum of one." ~ CRB, p. 138

From my pov, the intent and wording are pretty clear. If I had a lightsaber and felt like applying Jury Rigged to it, I'd probably up the damage by 1. YMMV.

Other modifications or talents that reduce advantage to crit specifically say "To a minimum of 1"

Jury Rigged however does not say this.

It does say that. You might want to read it again.

As a side note, I don't know if I'd allow Jury Rigged to work with Lightsabers. Not because of a power issue, but because they are already custom weapons, made by hand (or the Force or whatever).

Jury Rigged makes sense with mass-produced weapons, but Lightsabers are made by individuals, and I assume are already optimized.

I'm inclined to agree. Not just for flavor, but also power. Sabers are powerful enough already.

As a side note, I don't know if I'd allow Jury Rigged to work with Lightsabers. Not because of a power issue, but because they are already custom weapons, made by hand (or the Force or whatever).

Jury Rigged makes sense with mass-produced weapons, but Lightsabers are made by individuals, and I assume are already optimized.

You are absolutely right.

The thing is, lightsabers are weapons unique to the wielder. Jedi meditate during the construction, and through the force, each component is precisely tuned and altered on the molecular level so that it runs at near perfect efficiency. Altering a lightsaber in any way would cause it to cease functioning, or at worst, explode when activated.

Good idea for a house rule, that.

I think you should be able to use that on them.

However, remember that you could use Tinkerer on it to get 1 HP and give it the Superior quality, so that it automatically generates an advantage. That will make you crit practically all the time, instead of almost all the time.