One of the thing that you will notice that working with SharePoint Discussion Board you do not have ability to edit items using the Quick Edit. Based on my research Quick Edit option is only available when you have Standard View on your list. Since Discussion Board does not have Standard View Quick Edit option is disabled.
Doing research on this I came across this MSDN forums where the workaround was mentioned as using a PowerShell to enable Quick Edit on your Discussion Board list.
$web = Get-SPWeb “YOUR WEB URL”
$list = $web.Lists.TryGetList(“YOUR DISCUSSION LIST”)
$list.DisableGridEditing = $false
I have tried this on my development environment and it seems to be working but just word of caution, I am not sure if this method of enabling Quick Edit is supported.
So if you are using this approach I would advise you to validate if this is supported by Microsoft.