Mate, I am no expert on these matters as I have only been panning since January but I will share what I think I know.
Fellow members, if I am incorrect on some points feel free to chime in and correct me. It will be much appreciated.
Gold will travel down and collect in various places all along the river. Low points are a good place to check. Gold will sink to the bottom of cracks and crevices, behind boulders, etc: any point along a river where the fluid dynamics of the water flow allow gold to drop out of suspension.
Just because you are at the lowest point of a river does not necessarily mean the gold will be collecting there. The action of the water may actually push gold out of the hole and deposit it elsewhere. Large nuggets may be left behind though. It takes time to understand and confidently predict where gold will be. Best thing to do when starting out is to observe a watercourse when it is flowing to look for areas where the water flow slows down and then sample, sample, sample. Whatever you find in your pan, ask yourself why is it so?
I cleaned out a deep hole once and found a quarter gram nugget and not much else. A few meters away I panned 2.5g of pickers in four hours. Further down I found more flakey pickers and chunky fly poo pieces. Further still and I got flour gold. Half a k further down I was back into the pickers.
Obviously the larger, heavier pieces will drop out of suspension easier than lighter ones, which explains the progression of finds in the example above.
Why did I hit pickers again? Look around the area. Are there gullies, streams etc. feeding into the river? Is there a reef shedding gold into tributaries or from adjacent hillsides?
Look at the gold you are finding for further clues. Is it chunky with well defined features or is it smooth and rounded? Gold is soft so chunky pieces indicate that the source of the gold is close. Rounded bits may have travelled a long way down river or may be washing out of an ancient riverbed.
The river may have changed its course drasticly over time. With research and experience you may be able to discover were old flows were located. Often you will find old shafts dug near a river or even hundreds of meters away. The old timers were digging down to ancient alluvial gravels and following old water courses, looking underground for features where gold would have settled much the same as we do in current river beds.
Sinking shafts is way beyond my ken at this point...
So to answer your last question, it is worth digging anywhere you feel there may be gold. Even if you find nothing you will learn something. You never know if you don't dig it and you'll never learn if you don't have a go and make a few errors along the way. I have been surprised by the amount of gold found in spots dug for the hell of it and equally surprised by the lack of gold found in what I thought were perfect spots. Of course, others are looking for the same spots as you so it pays to think outside the box.
Thats a very brief summary for you. I recommend that you read through the relevant topics in the alluvial prospecting section for starters. There's a wealth of detailed information to get into. I can't remember the thread name but G0lddigg@ made a cracker of a post on where to look for gold in a river. Slaty Creek was the example he used. Many others have provided invaluable information too. Try searching keywords by clicking on the magnifying glass icon at the top of the page.
Best of luck,
Malcolm