I have a couple of tips that may be useful.
I have done a fair amount for evidence recovery. It is useful to add additional weight to keep you on the bottom.
Generally speaking the current is slower on the bottom due to friction loss by water traveling along the bottom. It is also somewhat slower along the banks for the same reason. You can find slower water around the downstream sides of boulders, etc. that create an eddy. Avoid diving near trees or log jams that can create a strainer that will trap you by holding you against it. We also utilize metal rods or probes sharpened at one end to hold us in place in the current by sticking them into the bottom. Long bladed screwdrivers work good for this.
Stay as streamlined as you can to avoid drag.
NEVER dive in water faster than 2 knots or you will get hurt. A simple way to roughly calculate the speed of the water is noted below:
Measure 100 feet along an embankment with a measuring tape. Throw in a floating object at the starting point upriver and time how long it takes for the object to travel 100 feet.
60 seconds = 1.0 knot
30 seconds = 2.0 knots
Keep your feet and fins from getting wedged in cracks, under rocks etc. as the current can tumble you backwards and you can get stuck or pinned underwater. Believe me, when the current breaks the seal of your mask or activated the purge valve of your reg, you should not dive it.
If you find something good, don't tell anybody where you found it.