Refer to the example image and the source, for some but not all of the arrows, the cylinder gradient goes from a light blue to either dark blue or purple, which seems to match the gradient color of the sphere below. This has happened unpredictably in various other cases, and unfortunately I cannot reliably reproduce this. Is this a bug?

I did'nt fully understand what's have been wrong.

I'd suggest you to use clones for such a work with many identical items. It would save time when doing slight modifications, and avoid such issues (don't forget to enable move gradients with objects option in selector tool).

Apologies if my description is unclear. The problem is that the cylinder on the lower right side of the attached (which I obtain by duplicating the asme object) somehow has its shading changed to look like the sphere below after some combination of saving, closing and reopening the image, whereas the same object in other cylinders don't. I can't reliably reproduce this, but this has popped up several times with similar objects, so I want to ask if there might be a deeper problem underlying this.

Your suggestion on clone is helpful and much appreciated.

I don‘t know why this happened - but it is easy to fix by selecting one correct object - then select a (or multiple) „faulty“ one/s and with cmd+shift+V „paste style“ will do it.

The only thing I can say, is that for the problematic linear gradients on "arrows cylinders", the stop are the same as the radial gradients used for the underlying circles. If you copy the circle, select the cylinder and paste style then click on linear gradient icon instead of radial gradient, you get the exact issue. Could you have made such mistake ?

Here is your file with the use of clones. selecting a clone and pressing shift+D will select the parent object. The power of clones is that you only need to modify the parent to alter all its clones.

I think that this svg contains information carried over from another project, such as 'context-stroke' in the fill style entries.

Also it does contain a couple of malformed paths. 

Thanks for posting the example, it threw an error in something I am working on, and enabled me to correct for a bug in my code. :)