I've soldered everything on, all my resistance/voltage checks, and they all came out fine. When I first did it I had a "deep hum" in the left channel, so I resoldered the pot and it went away. However, I still have a "buzzy hum", which stays fairly quiet when no audio source is connected, no matter how much I turn up the amp.
However, when a source is connected, even without anything being connected at the other end of the cable, a hissing occurs and gets louder the more I turn the amp up (maybe this is just a cabling issue, though) Forgot I had another RCA cable to test. It was indeed a crappy RCA cable.
I know this should be a grounding issue, so I resoldered all the connections that I could see that are ground connections. I've double checked this, and made sure that all other joints are soldered. I must have missed a ground connection somewhere for this to still be happening. The main joint I'm worried about is the ground coming from the power transformer, since it has a lot of connections in one solder. However, I have resoldered this and it looks fine. I have included
an image from the instructions, which has circled each of the joints I have resoldered. If I missed any or there's any more debugging I could be doing, please let me know.