So, what could be more important than mobility? Well threats are very important. It doesn't matter how mobile your pieces are, if you are checkmated. The player at the top of a club I was in once told me that 'Threats are what chess is all about!' Coming from such a strong player, this has to catch you attention.
What is a threat? Any move that can force a loss of material is a threat. A move that will cause checkmate is certainly a threat. Causing zugzwang can also lead to a winning advantage. Even something as simple as a loss of tempo might be a threat that needs attention in many positions. Any forcing move can be a threat, but it is important to see the resulting position well. If a forcing move, such as a check, has a good reply the 'threat' can be ignored. This can lead to bad mistakes in calculation! (ugh)
Threats are something that have to be looked for. Threats are another thing that can help you calculate more accurately, but you have to see them first!Being able to see threats that you can make will help you become a good attacking player. Seeing threats that your opponent can make will make you better a defensive player. That being said, it is obvious that you must see threats from both sides of the board.
The further ahead you can see threats and adjust accordingly, the stronger a chess player you will be. Now, if I can only get back into the habit of looking for them myself! ... Best of luck