From looking at the javascript it seems to use the same logic to generate the in worksheet dropLists as it does for the filter rows droplist. However the filter rows droplist is not transparent and causing that issue.
As far as CSS goes and if something is cascading down, I have removed all css files except the jmesa stylesheet for testing purposes. And the problem still exists for worksheet droplists, but not for filter row droplists.
Next I decided to look at the jmesa.css file since it must be the culprit. I downloaded the latest jmesa (3.0.4) I am currently running 3.0.3. And replaced the jmesa.css file I was using with the one from the 3.0.4 release. That seems to have fixed it. Doing a comparison of the two css files doesn't have anything sticking out as "this line is the cause", but switching to the 3.0.4 css file did fix the problem.
Now I'm going to switch out the js files to the 3.0.4 and just make sure everything still works smoothly with that. Hopefully nothing big changed with 3.0.4 that I can just upgrade and all will be good.
Hope this might help Lorie as well if she was using the 3.0.3 release.