A fantastic exercise for building up independent finger dexterity is the 'spider', as shown on John Patittuci's video.
Start by using the D and G string, one finger per fret, with your fingers about the 5th fret. Then play (finger numbers over the top of the TAB):
1 3 2 4 3 1 4 2
----7-----8-----5-----6-----
-5-----6-----7-----8--------
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Repeat this many times. Then move the pattern one string apart:
1 3 2 4 3 1 4 2
----7-----8-----5-----6-----
-----------------------------
-5-----6-----7-----8--------
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and repeat. Then one more:
1 3 2 4 3 1 4 2
----7-----8-----5-----6-----
-----------------------------
-----------------------------
-5-----6-----7-----8--------
and repeat.
Use a metronome, and start the pattern in quarter notes, making each note sustain to the next as much as you can. Move to eights and sixteenths, and then start speeding up the metronome.
Make sure you shake your fingers and hand out between runs - this is very stressful on the hand. also make sure you play lightly and with no stress in your left hand, especially as you speed up, because it's easy to start cramping your hand as you gain speed.
15 minutes of this for one week, and you will notice a massive difference - I promise!!