This Pebble started off with an intermittent fault that would gradually get worse - the screen would start to distort.
I had originally planned on removing the battery from this Pebble and transplanting to another Pebble Classic I had which couldn't hold charge, but on doing some digging came across a wonderful post (bless blogging!) that explained that this was a common problem and related to (probably) a loose (or not great) connection.
The solution: open the Pebble with a torx bit and insert a small slice of sponge behind the display and now it's running good and no screen garbage.