Since this issue was entered in Red Hat Bugzilla, the release flag has been
set to ? to ensure that it is properly evaluated for this release.

Fixed in http://projects.theforeman.org/issues/10356

This has been resolved in current 6.2 snaps, moving to ON_QA for verification.

FAILED QA:
everything is being displayed here just fine, but audit_comment stays 'null'.
This makes sense as the audit_comment links to a specific audit, not to the template.
So the payload should either contain whole history with references to the individual audit ids with their comments,
or audit_comment should show the comment of the recent audit.

# curl -u admin:changeme -H "Content-type: application/json" -X PUT -d '{"audit_comment": "foo", "template": "# my updated template"}' https://sat6.com/api/v2/config_templates/87
{"template":"# my updated template","locked":false,"snippet":false,"audit_comment":null,"created_at":"2016-05-18 11:49:57 UTC","updated_at":"2016-05-18 11:52:02 UTC","id":87,"name":"foo","template_kind_id":5,"template_kind_name":"provision","template_combinations":[],"operatingsystems":[],"os_default_templates":[],"locations":[],"organizations":[]}

The issue in comment #5 is a separate issue that is also present in the "get" version of the template json. 
audit_comment is only used for setting the audit comment, not displaying it. This behavior is inline with the UI - see BZ 1121577 for more info. 
If you believe this is a bug, please open a new issue. This issue has to do with inconsistency between the result of "GET" and "PUT" to the api - which is now consistent. 
Moving back to ON_QA.

Verified in Satellite 6.2 Beta Snap 12.

{
  "template": "<%#\nkind: snippet\nname: chief_client\ndescription: this is a single entry point for chef-client bootstrapping, it selects\n    a bootstrapping strategy based on host parameter named \"chef_bootstrap_template\"\n    note that it can be set per hostgroup, os, domain etc.\n    if there's no strategy set, omnibus is used by default\n%>",
  "locked": false,
  "snippet": true,
  "audit_comment": null,
  "created_at": "2016-05-25 15:35:15 UTC",
  "updated_at": "2016-05-25 15:35:15 UTC",
  "id": 111,
  "name": "chief_client",
  "template_kind_id": null,
  "template_kind_name": null,
  "template_combinations": [],
  "operatingsystems": [],
  "os_default_templates": [],
  "locations": [
    {
      "id": 2,
      "name": "Default Location",
      "title": "Default Location",
      "description": null
    }
  ],
  "organizations": [
    {
      "id": 1,
      "name": "Default Organization",
      "title": "Default Organization",
      "description": null
    }
  ]
}

Since the problem described in this bug report should be
resolved in a recent advisory, it has been closed with a
resolution of ERRATA.

For information on the advisory, and where to find the updated
files, follow the link below.

If the solution does not work for you, open a new bug report.

https://access.redhat.com/errata/RHBA-2016:1500