How to detect if meat (or any product) is not safe to be prepared as food? What are the marks that product is spoiled and not safe to cook or eat?
Besides obvious visual signs, like rot or bad smell of course.

The reason I'm asking is that I leave a meat in fridge for an extended periods of time, and  don't know how to track if meat is still safe to eat.
Visual signs and smells are an unreliable source for making this decision.  Foods can be contaminated, and/or unsafe, and you will be unable to tell by looking at a product or smelling it.  The only reliable ways to be safe are to (a) understand the source of your food, (b) ensure (or assume) that it has been prepared and stored properly before it got to you, (c) pay attention to packing dates and shelf life, (d) store the food properly yourself, and (d) cook your food properly.

According to foodsafety.gov (USA), in general, raw ground meat, poultry, and seafood has a refrigeration shelf life of 1-2 days. Raw roasts, steaks, and chops (beef, veal, lamb, and pork) have a 3 to 5 day shelf life, and cooked meat, poultry, and seafood can be stored in the refrigerator 3 to 4 days.