Full Idea
Regularity theories make laws molecular, with no inner causal connections; also, only some cosmic regularities are manifestations of laws; molecular states can't sustain counterfactuals; and probabilistic laws are hard to accommodate.
Gist of Idea
Regularities theories are poor on causal connections, counterfactuals and probability
Source
David M. Armstrong (Properties [1992], §2)
Book Reference
'Properties', ed/tr. Mellor,D.H. /Oliver,A [OUP 1997], p.171
A Reaction
[very compressed] A helpful catalogue of difficulties. The first difficulty is the biggest one - that regularity theories have nothing to say about why there is a regularity. They offer descriptions instead of explanations.