I saw a hole/dot in my Double Wall Tasting Glass, is it broken?

In short, no. 

These are vent holes and they are required during our manufacturing process, and they will not cause your glass to break during day-to-day usage. 

The holes vent the hot air to prevent the glasses from exploding during the manufacturing process since glass expands when heated. The divot's added to help equalize the air pressure when the glasses are cooling down. The holes are then sealed once the glasses have cooled.