Here is a link to the most comprehensive coverage of hardwood. The only dots I see are in the end grain but maybe someone else can chime in. BTW this type of wood is great for turning so it is very popular to make chess sets out of. Surprisingly it is not all that cheap and I bet someday will be a lot more expensive (read under pricing and availability).
http://www.wood-database.com/sissoo/
I like Sheesham, but I only own one set made from it. The problem for me has always been getting a set with good coloration, I love the deep, rich chocolatey brown. Many Sheesham sets (including 2 sets that I got refunded) are too light... looks like milk chocolate and isn't very attractive. I have seen the dots before, but not as prominantly as on your pieces. I don't personally find it to be unattractive, it adds character and is interesting. I wouldn't worry about it... I'd personally keep and treasure the set! 
I agree. The dots add character. This set is indeed darker than most Sheesham sets and I like it. BTW, I uploaded a set review in separate forum, if anyone is interested.
Thanks for sharing, and I like them. Very attractive. I can't say this for sure about your set, but some woods have parasites, most notably beetles. Some wood workers will fill the holes with wood putty, let it dry, then sand, and then go from there. Your set is fine however, even if that is what the little dots are. Possibly some type of reaction to the varnish, with the putty used.
I am guessing here, regardless, it shouldn't be a concern on such an attractive set. As you say, it adds unique characteristics to your set.
Once again, thanks for sharing, and best wishes.
Hello everyone!
I just bought a Sheesham chess set. Yeah, I know, most people don't like Sheesham, but I do. The grain reminds me of old school Soviet set that my grandpa used to have.
Anyway, my question is: what are those black dots on Sheesham wood?
There are a lot of them and I could not find them on any of Sheesham chess pictures online. Is there something wrong with my chess set?
I don't mind those dots at all, just want to make sure there is nothing wrong with the wood in my particular set.
Thank you,