I am making a two layer board. I have a ground plane on the bottom which is broken up by a few traces, and I have a power plane on the top side which is the same way.
Is having a power plane like that a bad thing?
It occurs to me that all the bypass caps I added may not be doing much if they're just attached to the two planes near the components because the power doesn't have to flow through them.
Then again maybe that's perfectly fine and the only real concern is having them on the plane near the parts they're supposed to smooth out the voltage for.
But I have no idea. So what should I do? Should I rip up the top layer and reroute it without the copper pour polygon, or leave it as is?
Only the noise on the power bus flows through the bypass caps, not the power. As long as they're near the power pins, they will do their job. In the configuration you describe, the board itself functions as a secondary bypass cap as well.
Have you verified that you have sufficient continuity between all of the segments of your power and ground planes? Without doing a careful analysis of the picture, it looks like signal traces may be creating some isolated power and ground "islands", or at least areas that are only barely connected together with thin bits of copper.
As geek said, the power doesn't go through them anyway. I noted in another thread however that your bypass cap for the shift register is too far from the power pin of the IC. Ideally you want the distance from the bypass cap your power pin to be as short as possible.
Ideally you want the distance from the bypass cap your power pin to be as short as possible
That is where surface mount capacitors come in to be very useful. You can place them on the underside between the pins or from the power pin to the ground plane almost as an afterthought.