http://www.nature.com/nature/journal/v207/n5001/abs/2071084a...
As you can read below, even with extreme care the Coriolis effect can be overwhelmed by very small perturbations such as how the lid is lifted.
http://web.aeromech.usyd.edu.au/history-chapters/C3%20Thermo... ...
> At Tom Fink’s invitation, Professor Lloyd M. Trefethen of Tufts University, USA, spent a short sabbatical in Mechanical Engineering in 1964/65. Already famous for his work on surface tension phenomena, he led us into a repeat of the experiments on the bathtub vortex that had recently been conducted by Ascher Shapiro at MIT. After much careful design, a circular tank of some 2.4m in diameter and 0.4m depth was constructed and installed in one of the subterranean dungeons of the old Peter Nicol Russell building. Carefully designed procedures and their diligent execution resulted in absolutely conclusive results that were published in Nature [Trefethen, et al, 1965). A re-enactment for the local media was a disaster: Bilger and Tanner muffed the removal of the covering baffles creating a great vortex in the water that then went out the wrong way. ‘Scientists baffled’ cried the media. We even made Time magazine!