That's the only place where I was able to information regarding JEHM and JIRA6 compatibility. Marketplaces states on 5.x but allows you to install it, your wiki is extreamly outdated not incuding information about JEHM 1.4 nor JIRA 6. Also, I wasn't able to find any clear bug on your tracker regarding Jira 6 compatibility, there is one but it states only 3 visual problems not real deal-breakers.
I think the Marketplace declaration may be confusing you, it refers to the most recent build, and is not specific to 'the latest' JIRA version. If you look, you will see that the last release was actually for JIRA 5.x not JIRA 6.x. So all information present is correct, all JEMH 1.4.x releases are tagged as JIRA6 compatible only.
The wiki is always being updated, if you have a specific problem, be specific with your question please. There is an upgrade page that written only a few days ago...
Regarding any JIRA6 specific deal-breakers, I'm not aware of any. There were some kinks to iron out initially but I think they have been dealt with. Following the upgrade guide above will help.
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