The difference between a modern replica and a double-knit authentic is mostly feel. Double knits are heavier than replicas... they feel more substantial.
As for visual differences, most teams use an off shade of grey and white, whereas replicas are just going to be standard grey/white. Team patches, commemorative patches and the MLB collar patch also are absent on the replica jerseys.
Replicas made prior to 2009 will have single layer numbers/letters on the back, but on the replicas I have seen lately, they have abandoned this practice.