The following is my professional opinion, and is what I work to here.
If you look at a mosaic which is labelled as ‘Roman’ what is it about it that makes this distinction? Well there are 2 stages to this;
1. The use of the Rules
2. The use of cut stone tesserae of slightly differing sizes.
1. The use of the Rules or Andamento, these govern the way in which the patterns and forms are set. The borderline of background tesserae used around figures is the most easily spotted. Without the application of this rule to a figural mosaic it will become a piece of modern work (and I don’t know of any figure mosaic from Antiquity which was set without this).
Take this to its extreme and you can have 2 people copying a Roman pattern. A 10 year old child using pieces of coloured card next to an artist creating a mosaic using stone tiles (tesserae) and Pozzolan (Roman cement) but without applying any of the Rules and the child would have the most authentic Roman mosaic.
2. Once you are applying the Rules the next stage it to use stone. Some floor mosaics had pieces of coloured glass in them, some (particularly in Roman Britain) utilised cut up roof tile or pottery for the red colours but 99% of the material used was natural stone.
There is a skill to matching colours particularly in figural/portrait work but the main skill you need to acquire is to be able to with tesserae that may be all of the same average size but every piece is slightly different in its overall size, (please refer to my article on backgrounds).
So, 2 areas, the first is you need to apply the Rules in setting your mosaic, next you need to be able to use individually cut tesserae. Using wholly machine cut stone cubes (i.e. every face is 10mm x 10mm) is a different thing all together and it is very difficult to lose the straight edges.