Spot Reduction Myth
Contrary to what the info commercials suggest, there is no such thing as spot reduction. Fat is lost throughout the body in a pattern dependent upon genetics, sex (hormones), and age. Overall body fat must be reduced to lose fat in any particular area. Although fat is lost or gained throughout the body, it seems the last area to become lean or the first area to get fat is the midsection (in men and some women) and hips and thighs (in women and few men). Sit-ups, crunches, hip raises, leg raises, hip adduction, hip abduction, etc. will only exercise the muscles under the fat.

Incidentally, fat is also stored under the abdominal muscles and around the intestines and other organs. This can contribute to the "pot belly", pushing the abdominal muscles and the overlying fat outward. This "apple shape" fat distribution has greater health consequences than the lower body "pear shape" fat distribution.

Lower Abdominal Myth
It is widely believe the lower abs are exercised during the leg raise or other hip flexor exercises. It can be misleading to judge the mechanics of an exercise based upon localized muscular fatigue. The primary muscle used in hip flexion is actually the Iliopsoas, one of many hip flexors. The Iliopsoas, indeed, does happen to originate deep below the lower portion of the Rectus Abdominis. During the leg raise the entire abdominal musculature isometrically contracts (contracts with no significant movement) to:
 

• Posture the spine and pelvis
• Supports the weight of the lower body so the lumbar spine does not hyperextend excessively
• Maintains optimal biomechanics of the Iliopsoas
• Hips are kept from prematurely flexing if the lumbar spine and pelvis does not hyperextend excessively 
• Iliopsoas can contract more forcefully in a relatively slight stretched position 
• Bent knee (and hip) situps actually place Iliopsoas in a mechanical disadvantage 
• Counteracts Ilopsoas's pull on spine 
• Many people with weak abdominal muscles are not able to perform hip flexor exercises without acute lower back pain or discomfort 

High Repetitions Burn More Fat Myth
Performing lighter weight with more repetitions (15-20 reps, 20-30 reps, or 20-50 reps) does not burn more fat or tone (simultaneous decrease of fat and increase muscle) better than a heavier weight with moderate repetitions (8-12 reps). Weight training utilizes carbohydrates after the initial ATP and CP stores have been exhausted after the first few seconds of intense muscular contraction. Typically a set's duration is 20 to 30 seconds. For the average fit person, it requires 20 to 30 minutes of continuous aerobic activity with large muscle groups (eg. Gluteus Maximus and Quadriceps) to burn even 50% fat; fat requires oxygen to burn. Performing a few extra repetitions on a weight training exercise is not significant enough to burn extra fat and may in effect burn less fat. If intensity is compromised, less fat may be burned when light weight is used with high repetitions. The burning sensation associated with high repetition training seems to be the primary deterrent for achieving higher intensities.

For individuals attempting to achieve fat loss for aesthetics, the intensity of weight training can be a double edge sword. When beginning an exercise program, muscle mass increases may out pace fat losses, resulting in a small initial weight gain. Significant fat loss requires a certain intensity, duration, and frequency that novice exercisers may not be able to achieve until they develop greater tolerance to exercise. If an exercise and nutrition program is not adequate for significant fat loss, a lighter weight with higher repetitions may be recommended to minimize any bulking effects, although less fat may be utilized hours later. If an aerobic exercise and nutrition program is sufficient enough to lose fat, a moderate repetition range with a progressively heavier weight will accelerate fat loss with a toning effect. If a muscle group ever out paces fat loss, the bulking effect is only temporary. For a toning effect, fat can be lost later when aerobic exercise can be significantly increased or the weight training exercise(s) for that particular muscle can be ceased altogether. The muscle will atrophy to a pre-exercise girth within months. Higher repetitions training may be later implemented and assessed.

It still may be recommended to perform high repetitions (20-30 or 20-50 reps) for abdominal and oblique training. With fat around the waist, moderate repetitions with a greater resistance can increase muscular girth under the subcutaneous fat. If fat is not lost, more muscle can push out the fat resulting in a bulkier appearance. The abdominal muscles are relatively small muscles. Performing high reps with a lighter resistance will not compromise metabolism or muscle increases as would performing high reps with light resistance on larger muscles. See Spot Reduction Myth above.

It is plausible that the high repetition myth was originated and later propagated by bodybuilders that used calorie restrictive diets to shed fat before a contest. Because of their weakened state from dieting, they were unable to use their usual heavier weights. When inquired about their use of lighter weights, they explained they were "cutting up" for a contest. This is merely a theory, but it is easy to see how it may have been misunderstood that the lighter weight was used to reduce fat instead of actually being a result of their dietary regime.

From exrx.net