Translation:That building does not have an emergency exit.
To say 'no tiene una salida' would mean there is not one, but possibly zero, two, or some other amount. So to specifically say none at all, you just drop the article.
Can someone explain the difference between this sentence, and one which would mean "This building has no emergency exit."? That is the way I translated the sentence, and I recognize that I was too informal. I'm just curious if it is even possible to form a sentence saying that in Spanish. Would it be Ese edificio tiene no salida de emergencia?
"This building has no emergency exit" and "This building does not have an emergency exit" would be the same in Spanish. The issue with your sentence in relation to this problem could be that you have "this" instead of "that."