The most common mistakes I see people make in their homes has to do with scale. I have seen countless clients downsizing and trying to bring their over-sized furniture with them, only to discover that none of it fits in their new home. When you downsize, you need to also downsize your furniture so that your space doesn't feel overwhelmed.
If you are considering downsizing make sure to measure your furniture and measure your new home before you start to move. There's nothing worse than carting an 11 foot sofa to your new home to find out it won't fit and it will have to sit outside until you can figure out what to do with it.
It might be worth the money to hire a designer to do this work for you as well. A designer should be able to measure your existing furniture and measure your new space and let you know what pieces you should take with you and what pieces you should sell or give away.
Another rule of thumb is to only bring quality furniture with you. That table from IKEA should not come with you, there's no sense in keeping low quality furniture like this in your new home. When you downsize and move into a smaller home, the small details like the quality of furniture will become more apparent in your new home since there will be much more valuable real estate in a smaller floor-plan.