Here’s an update.
1) I was able to determine the cause of the cookie error message and correct it. The problem occurred immediately after I added a new site in Multisite, which I have configured in “sub-domain” mode, but in which each site is presented as a unique full domain (a.com, b.com – not a.c.com, b.c.com) Each such domain is “parked” at my ISP. The last step in establishing a new domain is to obtain the well-hidden site id, then enter this into the panel presented by WordPress MU Domain Mapping plugin. I’d simply forgotten to do this last step. When I backtracked and did that, the login worked normally.
2) So, I’ll retract my characterization of this as a “bug” in the core. However, it certainly seems to me that the existing implementation is flawed in its handling of this situation and could provide better diagnostic information.
@sader I started this thread to let you know that the problem was not related to your plugin.