Very High Resolution Sensor: 20.0MP Nikon L28's 20.0MP sensor will provide larger room for cropping, and you will be able print your portrait shots larger with more fine detail.
Small 1/2.3″ (6.16 x 4.62 mm) sensor It is difficult to achieve that shallow depth of field and blurry background for your portrait shots with a small sensor.
No Image Stabilization Lack of Image stabilization may result in blurry photos especially in long exposures and at long focal lengths
No RAW shooting capability RAW files contains more color information compared to JPEGs, so it is easier to get a natural skin tone and colours during post processing, which is very important for portraits.
No External Flash Shoe Use of External flash creates many creative lighting opportunities for portrait photography and built-in flashes are almost useless for portrait shots.
No Built-in Viewfinder In the lack of a a viewfinder, holding the camera away from the body while using live view is not very stable, especial with heavy camera bodies and lenses. Besides, LCD screens are very hard to read under bright sunlight.
No Manual Focus Mode You have to nail the focus perfectly for a good portrait shot. Compact cameras are not great at focusing at low light and complex lighting conditions, so manual focus mode is very useful at these times.
No Manual Exposure Mode A correct exposure of portrait model is crucial. Even though modern digital cameras features advanced algorithms to calculate the right exposure, they still may fail some difficult conditions. Lack of manual exposure mode in these conditions means lot of shadow and highlight clipping.
Not so good Ergonomics&Handling Good handling and existence of well placed physical controls on the camera body is very important during portrait shooting. It is faster and more intuitive to change the camera settings with dedicated buttons and knobs instead delving into the menus on the LCD.