If you are playing fast, anchoring your fingers just won't cut it. After you have held a certain note for it's duration, start moving that finger to it's next note in whatever pattern you're playing. This way, the finger will already be directly above it's next fret when it's time to play the note. It keeps the tempo fluid.

For example, if you are playing a simple A Minor scale...

|-----------------|
|-----------------|
|-----------------|
|-------------5-7-|
|-------5-7-8-----|
|-5-7-8-----------|

Once your ring finger has hit the B note on the E string, your index finger should be up and on it's way to the 5th string to catch the D after your pinky gets the C. If you hold your index finger on the A until it's time to go to the D, there will be a gap between the C on the E string and the D on the A string.

On the note that it hurts your tone, it can if you let your technique be sloppy. You must wait until your ring finger is solidly in place on the string before moving your index finger or you will get unwanted noise... if you practice correct technique, however, this shouldn't be a problem. Hope this helps...