I'm gonna go through this line by line.
Create New Ticket interface - public + admin
Actually, it would use the template system, so that it can be themed to the individual site
Auto Ticket numbers
This is easy, simply use the mysql id number
Departments - admin
Um, HCL already has these... We can reference an HCL dept.
Operators; assignable to Department - admin
Ditto, already handled by HCL.
Full email integration; pull tickets from a mailbox into the interface and send emails out from the interface - admin
Shouldn't be too difficult. This is mostly pretty standard PHP code.
Assign ticekts to an operator - admin
Ok, and maybe have it optional for operators to assume unclaimed tickets.
Assign Status to Ticket - admin
again, some people want ops to be able to do this, so maybe a config switch.
canned email responses - admin
Ticket status checker- public (would be great if the login could be pulled from a referring form or Querystring)
Or maybe just a link that is sent with the first report of the problem, let them click the link and look up the problem. Use a random MD5 hash to use for authentication, then they don't need a "login"
Ticket Status Log - admin (include status changes, answers (via email), notes added // all entries need user, datetimestamp, detail)
Again, makes sense for an admin overview.
Ticket Flags - admin
What purpose are you thinking about?
Ticket filters - admin (by status, date added, email address, title, operator, etc.)
Hmm, I can see this being needed by ops as well, if you have a lot of tickets. It would be more of a sort and filter.
Ticket system banning - admin (stop spam)
Initially yes, but once 2.2.x comes around, it will have built in banning, if their spamming the tickets, you probably don't want to live help them.
Transfer ticket between operators - admin
Again, maybe a switch to allow ops, some will want it, some won't.
Alerts (change of status (sent to client), or transfer emails (sent to receiving operator))
Yes, very important. Thinking that when the new windows/linux native app is done, allow this to interface in as well.
On the advanced idea, that will be possible in 2.2.x, and maybe in 2.1.x (future versions).
All in all great ideas!