Slight wobble/"drift" in chain due to crankset? A few months ago I replaced the bottom bracket on my 2002 Fuji Finest. After reassembly I noticed the chain "wobbles" slightly when pedaling. You can see in this video the chain drifts toward the outer edge of the derailleur during rotation. 


                
            

I assumed the issue is caused by one of two things: 1) the BB; 2) the crank.

Here is what I've attempted so far:


I had another, new BB available. Thought maybe Bracket A was wonky. Both are Shimano square taper brackets new out of the box. I replaced bracket A with bracket B, reattached the arm. Still wobbles.
I had a spare, new crankset available out of the box. Thought maybe Crank A was bent. I tried Cranks A and B on both brackets A and B (so combinations of AA AB BB BA). Still wobbles.
I reseated both cranks on the BBs. The bolts are on tight and the crank itself feels solid. Still wobbles.


At this point I'm a bit stymied. I accept that the bike is rather old, and the bike still functions just fine (I've put a few hundred miles on it since the BB replacement). My main concern is the wobble may get worse if not addressed now.

Any thoughts on this? I appreciate the insight of the more technically adept!
The amount of wobble shown in the video is fairly typical, for better or for worse, which is not to say it's a good thing or that the FD adjustment can necessarily be free of rub in all combinations and under variable load with it. You don't have to worry about this getting worse if you leave it alone.

For what it's worth, you can multiply your "AA AB BB BA" set by four, because the rotational position that a crank is mounted on a spindle determines how bad the total wobble is, and making things truly as close to perfect as obtainable requires you to test all of them. I don't recommend actually doing this in most cases, but it is true that one position will be the best, possibly to an extent that matters.

The nature of runout in a square BB spindle is that the mounting orientation 180 degrees different will distort the chainring the same amount the other direction, meaning that one orientation's error might stack with any imprecision in the crank in a way that maximizes the effect, but mount it the opposite way and the two could cancel each other out and look great.

For cranks with rings mounted on different sets of bolt holes, i.e. most triples but not most doubles, you can observe whether all the rings are moving in unison to draw inferences about whether a given bit of distortion is coming from the spindle or the crank. And of course, even on a double, you can compare what's happening between the two rings to infer whether you're looking at error in the spider tabs or the rings themselves.

Spider tabs can also be trued. Before doing so it's important to do some kind of testing or measuring to make sure it's not the BB or chainrings that are causing your problems.