Not the likes of Georgette Heyer (not truly trashy IMO), but the really indefensible.
Mine is Cassandra Clare - I'm currently eking out her latest book, ignoring the massive plot holes (and improbable lack of communication without which things would be resolved in about 2 chapters) in the certain knowledge that it'll no doubt end on a cliffhanger which won't be resolved until book 3 in about 2 years time.