Lifehacker reader meseta offers a quick, clever method of cleaning inside hard-to-clean containers using water, soap and a little rice:
This tip is from my mother from many years ago, when she had to clean an awkward ring-shaped milk bottle for my then baby brother: Use raw rice to clean tall or irregularly shaped bottles that have difficult-to-reach areas.
Fill the bottle with a little water, some rice and a tiny amount of dish soap/detergent; fit the lid or just cover with your hand and SHAKE! The rice is hard enough to scrub any residue from the side of the bottle. Sometimes, when she had to face tougher stains, she would use the ball-chain from her ID pass instead of rice.
Great for jars, vacuum flasks and baby's milk bottles.
I gave this a try this morning on the carafe in the picture and it seemed to work, though this method's probably suited to smaller containers.