The problem seemed to end up being the empty set returned here:
mysql> select * from OS_CURRENTSTEP where ENTRY_ID=(select workflow_id from jiraissue where pkey='<issue id>');
Empty set (0.00 sec)
Issues I did not have the problem with had a row returned by this sql and issues I had the problem with returned an empty set.
So I am a bit confused ... Did you solve your problem?
If not could you send me a screenshot of:
1) Issue causing the proble in the taskBoard
2) Same Issue standard issue view
Also can you make sure that you are actually capable to transitate the issue via the JIRA standard Issue screen.
If not you might want to log a support ticket to Atlassian