The correct use would probably be "°C" and "°F", respectively.

Fixed in cvs

They were marked for translation, which breaks gettext since the
degree symbol (°) is not ASCII
(http://developer.gnome.org/doc/tutorials/gnome-i18n/developer.html#use-ascii):

The messages containing those symbols ("°C" and "°F") should probably
not be marked for translation because of this.

Only the C and F are marked for translation. The degree is displayed
from it's unicode value I think.

Here's the relevant code:

degree = N_("C");
tmp = g_strdup_printf ("%d/%d\302\260%s", high, low, degree);
gtk_label_set_text (GTK_LABEL (applet->labels[i]), tmp);

So the \302\260 gives the degree symbol. Let me know if the F and C
should not be translated.

Sorry, yes the warnings come from these two messages:

  tmp = g_strdup_printf (_("%s\nToday: %s\nCurrent temperature
%d\302\260%s"), 
                applet->gweather_pref.city, get_conditions(info->wid),
                info->curtemp, degree);

  tmp = g_strdup_printf (_("%s\n%s: %s\nLow %d\302\260%s, High
%d\302\260%s"),
                applet->gweather_pref.city,
                forecast->day, 
                get_conditions (forecast->wid), forecast->low, degree,
                forecast->high, degree);

Including non-ASCII characters in messages marked for translation, be
they octal escaped or not, doesn't work.

I think that °C and °F should not (or cannot) be translated because
both symbols are derived from a person's name (Celsius and Fahrenheit).

Fixed now. It's no longer translated.