Check what Alex said first, but there's one thing that trips up a lot of people (the UI design seems to fail a lot of users here, not sure why, when the rest of Confluence seems to work ok)
When you go into "Edit and Share Filter", you'll see
The thing that seems to confuse a lot of people is that this LOOKS like the filter is shared with everyone, but they don't realise that you actually need to click "add" before the sharing is enabled (and "save" of course)
Supposing you're using jira 5.x ...
AFAIK the only permission related to this is "create shared object", and is granted to you if you are able to share the filters ...
With the other users, can you go to Issues, Manage Filters, Search and perform a search for filters owned by the first user?
Are you sharing to a group or to anyone?
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