I got a reply to my last bug report, acknowledging that it’s a bug and saying they’d send it on to their engineers.
Here’s another:
The first one should only evaluate to zero if it’s zero for all a,b. The second indicates that that’s not the case. This one cost me several hours, as I searched elsewhere for why my results didn’t make sense. (The offending bit was originally in the middle of a larger expression; otherwise, I would have figured it out more quickly.)
Update: The Mathematica people have acknowledged this bug and passed the word on to their developers, presumably to be fixed in the next version.
Update 2: Two years later, I got an email saying that the bug had been fixed. I can confirm that, as of Mathematica version 10.4, the problem is gone. It was still there in 10.0. I didn’t check the versions in between. The previous bug involving the spherical Bessel function is still there.