1. I would bet that your thumb is sticking up over the back of the neck. Stop that. If should stay roughly along the "equator" of the neck and pretty much directly opposite your second and third fingers.
2. I would also bet that when you fret a note your finger is closer to the back of the "fret box" in the direction of the nut. Stop that too. Put your finger up as close to the fret wire as you can without being right on top of it. That will minimize the buzzing that can occur from not having enough pressure of the string on the fret. Your tone will improve too.
3. I would bet that your pinky, ring and middle fingers fly away from the fretboard when you aren't using them. Stop that! Keep your fingers down even when you aren't using them. Try this exercise:
Put your first finger on the 7th fret of the E string and play 1 finger per fret 1-2-3-4. Then play that same pattern on the A string, 7th fret and on up across the neck. Not too difficult, eh? Ok, now play that pattern _very slowly_, and leave your fingers pinned down until you absolutely have to move them. That means when you move from the E to the A string with that pattern your first finger will be on the 7th fret A, but your 2nd, 3rd and 4th will still be stuck holding down the previous 3 notes on the E string. Feel the burn?
The next place to take that pattern is up to the 12th fret and play E 12th fret, A 13th, D 14th and G 15th all the while keeping your fingers down. Then reverse that pattern (G 12, D 13, A 14 and E 15). Speed is not the goal here. Accuracy and cleanliness is.
Also try adjusting your strap to the same height your bass sits as when you are sitting. Bass hanging around your knees might look cool but you sure can't play it very well like that. It's like a short guy adjusting his driver's seat all the way back.
I think the problems you have is a weak fretting hand and the symptoms you describe are compensations for that. Do those 2 above exercises for 15 minutes every day as a warm up (s l o w l y) and you should see some great improvement in less than 2 weeks.
Post a follow up and let me know how it works.
