Some things to look for in a new digital camera from a photographer's perspective. These are the features and functions I would value in a P&S camera.
• Wide zoom range. Long lens i.e. equivalent to around 400 mm on a 35mm film camera and a wide angle equivalent to around 35 mm in a 35mm film camera.
• With a long lens comes the need for (IS) Image Stabilization unless you plan on carrying a tripod around with you. It is very difficult to hand hold a 400 mm lens and get a decent photo without IS.
• IS is also important in low light settings.
• A wide aperture range is very important. It allows you to control (DOF) Depth of Field (i.e. f2.8 - f4.5) I can't emphasize the significance of this strongly enough.
• Long battery life is also a consideration. Cameras vary widely in the number of shots it can take. Most photogs prefer a camera that uses AA cells as in a pinch you can always pop in some alkalines that are available anywhere.
• Size, shape and location of the controls. Is the camera easy to use and comfortable in your hands?
• Speed of operation. How fast can it be ready to take the first photo and how fast does it take the subsequent shots? You don't want to miss shots because the opportunity was lost while you were waiting for the camera to become ready.
• How fast does the camera achieve autofocus lock in various lighting conditions?
• Full manual control. There often are times when the various autos functions just don't choose the right settings.
• A macro ability that focuses down to 1 cm.
• A large bright LCD to allow you to see it in bright light and easily make feature changes in bad lighting conditions.
• An optical or EVF viewfinder. An LCD is not usable in bad lighting conditions (i.e. in full sun)
• A hot shoe to allow you to add and external flash. This is especially important if you do portraits or a lot of indoor photos of people.
• Custom white balance. If accurate color is important to you, the need for this feature is critical.
• The number of Megapixels. The difference between a 5MP and an 8MP camera is largely insignificant in the final photo. The difference between 3MP and 5MP is more significant.
Check out this
Buying Guide for help in side by side comparisons of cameras.