If I overstay and pay the fee, does this make any sort of black mark on my passport / records?

[Bajo_cero2]

Hi, recently joined, loving the forum and the sense of community. Kudos, especially to the regular contributors! Got me seriously thinking about taking the plunge... still researching.

Would I be right in assuming that a lot of potential problems in overstaying on tourist visa go away if you have 2 passports? (Don't hurt me, family lineage has its perks!). i.e. overstay on one, leave... come back on the other.

No.
Overstaying is not illegal in Argentina.
Visa runs are illegal.