After putting up with issues from the brcmsmac driver, I decided to give
the proprietary driver a go.  The (wl) driver seems to work just as well
as
the brcmsmac driver on the prior packaged 3.12 kernel, but is more or
less unusable with the 3.13 kernel.

I cold booted with 3.13-1 and was able to authenticate and associate
with the access point.  Some initial traffic flew across the wire, but
then the card appeared to lock up while the tools were unaware of the
issue.  Connections began to time out while the software thought the
connection to the AP was still active: I was unable to even ping the
gateway.

The following was logged in the kernel log shortly after booting.

[  363.615975] ERROR @wl_cfg80211_get_station : Wrong Mac address
[  363.616052] ERROR @wl_cfg80211_get_station : Wrong Mac address