This appears to be happening because the issue show action has a custom view (show.builder.xml) that is including the issue's relations, custom fields, etc. whereas the JSON format uses default to_json method on the issue model which doesn't include those things.

I'm going to tackle this by moving the XML builder code into the issue model's to_xml method instead of a view file. Then I'll make the issue's to_json method just call the to_xml method and convert the XML to JSON so we only need to maintain the serialization code in one place.
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I think this patch addresses the issue. The changes are also available at http://github.com/asoltys/redmine/tree/issue_serialization
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This is a real problem with using the XML views. Instead of overriding @to_xml@, I'm wondering if there is a common method we can make so both XML and JSON formats are always the same. Example:

<pre><code class="ruby">
def to_xml
self.to_api_format(:xml)
end

def to_json
self.to_api_format(:json)
end

def to_api_format(renderer)
{
:id => self.id,
:subject => self.subject,
# ....
}
# ...
end
</code></pre>
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Fixed in r4458. xml and json responses now use the same template.
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duplicates,Closed,7158,Issues Custom fields not in json