Mild winters mean more chimney fires! It's true. People choke back their woodstoves in mild weather - leading to more creosote accumulation - but many don't realize this, so they skip getting it cleaned, thinking it doesn't need it as bad as it would after a cold winter.
Loose or sagging plastic gutters will not drain properly, and this may cause their contents to overflow. As a temporary measure, hammer in a wooden wedge between each bracket and the gutter to hold each section in place until you can replace it.