I can't emphasize how important proper form is. Proper form will enable you to get the absolute most out of each set and totally fatigue the intended muscle group. Improper form will often bring ancillary muscles into play decreasing the effectiveness of the exercise and wasting most of your effort. For example, have you ever seen a lifter with well developed pecs who bounces the weight off of their chest? Or a bodybuilder who uses mostly back during a squat with large well developed legs? Probably not on both accounts. Improper form often occurs when the lifter is more concerned with the actual weight they lift instead of form. These trainers are wasting their time by cheating their way through the exercises and the heavy weights they claim to lift are mostly false bravado. Good exercise habits begin early but are never to late to correct. If you feel that you have poor form you can correct it by performing the exercise in front of a mirror for self critique or have a seasoned lifter or personal trainer at the gym show you proper form.
If you want to speed up your workout at the gym to increase the cardiovascular benefit or you're in a time crunch then decrease the time in between sets. Never perform your exercises faster to save time. You'll only end up compromising your form and leave yourself susceptible to injury.
