People who trust their own judgement, enjoy finding new and better ways to do things, and prefer to be evaluated more on performance than politics are happier and more productive in these organizations. In organic ones, people share it. So ask how much information sharing goes on. You can confirm this by calling the organization with a question and seeing how many people you have to talk to before you get an answer. The more handoffs in your bureaucratic relay conversation, the more mechanical the company probably is.
Mechanical organizations isolate people in their departments.
Organic ones support wide-spread networking. Mechanical organizations usually develop new products in a more centralized way than organic ones. At 3M, a very organic company, almost anyone can come up with a new product. More mechanical companies are likely to do so in a dedicated department or special units in several operating departments. No one of these issues alone can tell you how mechanical or organic an organization is.