The final drawback to using a teleconverter is reduced image quality. The converter adds more glass elements to the optical path, and this tends to reduce sharpness and contrast, and increase aberrations and vignetting. Higher-end converters matched to higher-end lenses minimize this—pros often use converters—but you probably don't want to put a cheapie 2x converter on, say, an 18-200mm superzoom if you want optimal image quality.
USING A CONVERTERRead the instructions for your converter, as well as for the lens you intend to use with it. Most converters are designed to be used with specific lenses or a specific range of lenses (generally, telephotos and pro telezooms). In some cases, attaching a specific converter to a specific lens can damage the lens and/or converter, so be sure to check the instructions for both before attaching.
It's best (and with some systems, necessary) to attach the converter to the lens, then attach the combo to the camera body. If you attach the converter to the body, then attach the lens, the body may not recognize the converter, and you'll get an error message. Be sure to switch off the camera's power before attaching or removing lenses and converters.
Since you'll be getting really long focal lengths when using converters, be sure to use proper long-lens shooting technique. It's best to shoot from a solid tripod. If handholding, select a fast enough shutter speed; converters increase the effects of camera shake along with the focal length. The old rule of thumb from film days—use a shutter speed of at least the reciprocal of the focal length (e.g., 1?500 sec. with a 500mm focal length)—isn't good enough for high-megapixel DSLRs (where the image can be blown up a lot) and cropped-sensor cameras (which effectively increase focal length). If handholding a DSLR with more than 10 to 12 megapixels or a crop-sensor camera, use a shutter speed equal to at least twice the focal length (e.g., 1?1000 sec. for a 500mm lens). This will require use of a higher ISO setting, but as noted, today's DSLRs produce much better image quality than film at higher ISO settings. Lenses and cameras with image stabilizers are a big help here.