In a perfect world, nothing would ever go wrong with your mattress. But when problems do occur, often they can be alleviated or prevented from becoming bigger problems.
If your mattress has sagging in the center, make sure it is in a frame that has adequate support in the center of the bed. This generally means a bar down the center of the frame that has at least one leg (and preferably more than one) supporting it from the floor. Today's mattresses are heavy, and the number one cause of sagging in the center of a queen size or larger mattress is inadequate support from the foundation and/or the frame.
The reality of today's mattresses, which are often made with layers of padded material, is that the layers of padding compact over time. Body impressions in the first 30 days of owning a mattress should not occur and could be a sign that there is a flaw in the mattress. But within the first year, it's not outside the norm for certain types of mattresses with a lot of padding (and particularly if the padding material is of a lower quality) to develop body impressions.
The way to combat body impressions is to be diligent about rotating your mattress. No-flip mattresses are typically the ones with padding on one side, and so those cannot be flipped. But they can be rotated a half-turn every 3 months in the first year and every 6 months after that. Because partners are often of different weights and because the upper body weighs less than the lower body, rotating your mattress regulary will stave off the development of impressions that form when the weight of the body compacts those layers of padding over time.
Mattresses made with memory foam, gel memory foam, and synthetic latex typically receive the most complaints about off-gassing, or release of chemical odors. These odors dissipate over time, and should be gone within about 30 days. If you can, experts advise leaving a new mattress open to the air in a well-ventilated room for 2 weeks to allow any odors to dissipate.
When a new mattress is first delivered, it's not uncommon for people to comment that their new mattress feels firmer than the one they tried and loved in the store. The reason for this is that the floor model in the store has likely been tested out by many customers, which softens up the feel of the mattress. Over time and with regular use, your mattress will feel less firm than it does when it's brand new.