What is the meaning of Dimer Catastrophe?
A "plasmid dimer" is defined as a plasmid that has two origins of replication instead of the usual one origin of replication. This can happen if two copies of the same dimer undergo recombination resulting in one plasmid with two origins and one with zero. I hadn't seen this term before, but it seems to be the meaning with which it's used in this paper and a few others I saw.

The "dimer catastrophe" hypothesized in this paper refers to the idea that over time this would lead to a reduction in overall plasmid copy number (and thus an increased probability of plasmid loss), since dimers may be more likely to replicate than monomers (due to having more origins of replication).

For what it's worth, I also found the paper you linked a bit hard to understand, but I found this one more explanatory (your mileage may vary): Multicopy plasmid stability: Revisiting the dimer catastrophe.