One prob is the top grade stones are usually exported and the cheaper stones are mostly sold off to the tourist market. Here are some examples:
A good(but not great) Larimar stone:
A medium grade stone (bad cut though and possible crazing)
A "tourist" grade stone in a cheap mounting:
The higher grade stones can be almost indigo in color with clean milky white veins through it and may or may not have Chatoyancy, which gives the stone a depth to it and has it shift color slightly in strong light. The first stone has a AAA section to it and would be worth quite a bit if it were more uniform. It has a few flecks of matrix, but they are only on the edge where the mounting would cover it.
The DR also has some very nice(and large) amber, but again, you have to be careful of what you buy. I brought back a 100 gram necklace that I bought from a good dealer for $100 and sold it within a week after I got back for $300. The main thing to look out for in amber are any stones that have bugs in them as they are always fake in tourist shops. There are numerous tests for amber including putting it in some salt water. The real stuff will float. My quickest test is to touch it to my teeth. Plastic is harder and you can tell real from fake pretty quick that way after you compare them. Any green or reddish amber may be real, but is likely imported from Europe. Dominican amber is more "beer" colored, from a light Pilsner to Guiness in color.