Tom, heres a list of the small things I have found in getting the component up and running on my site - in no particular order. I hope you find them helpful.
Best wishes
Rich
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Global Parameters:
\"Show\Hide Study title on view page\" has wrong choices copied from item below (show verses and chapters)

Menu manager: menu item parameters - component: Page title here does not save if changed (but saves okay in global paramaters and then displays here correctly) \"Page title\" is also in Parameters- system below so could be deleted from here or greyed out or \"use global\"
Study view appears here in menu manager as a choice, but it doesn't work directly from a menu item.

Module display:
A study with no media displays a broken image \"X\" in IE where the media icon should be - Firefox handles this with no problem.
The html shows the img src is being set as the base url:


Joomla search:
Series names do not return results in joomla search (assume same for topics, books etc?)

Topics:
Missing from all the views, column entries etc, except search - could be intentional but mention it as all the other entries are options in the lists, might be useful for someone.
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Date formats, not a bug but a nice to have:
None of the formats are European\UK convention of day-month-year - spare a thought for us Brits

Series and Teachers: not a bug but a nice to have:
would be great to have a description field for these that would optionally display in the study view: or at the head of the search results view if soemone chooses the series from the drop down. as an example For the teacher a likely use would be a short biog.