Barracuda Outbound Queue

I'm also using the same Barracuda Spam and Virus Firewall 300 and have seen this issue come up.

From what I've seen, while transferring emails with a large attachment the connection to the receiving server will sometimes time out before the transfer is complete. This is dependent on the upload speed you receive from your ISP.
If it times out the transfer then needs to be restarted all over again. The appliance will only transfer 1 or 2 messages at the same time. So if a sender copies 10 people with a large attachment the mail is queued 10 separate times to transfer to each recipient. This can hold up the other messages in the queue resulting in the high out-queue alert.

I think the setting for this timeout is under the Advanced tab and then the "Remote IMAP/POP" settings.
I'm not 100% sure if this is the right setting but I can't find an outbound timeout anywhere else. Try raising the timeout there (ours is set to 320) and see if it has any effect.
Setting it particularly high is not recommended but I can't recall the exact reason why.

That doesn't seem to be making a difference for us. I did find this error when doing an SMTP Test on Barracuda.

Outbound SMTP Connectivity  
Error: Could not send email to a host outside of your network. This could interfere with sending bounce messages from your Barracuda Spam & Virus Firewall. Please verify that your network permissions (firewall) allow SMTP traffic from your Barracuda Spam & Virus Firewall to the Internet.

You'd need to find out whether that Outbound SMTP error was for a host that you should have been able to send mail too or not.
Often spam and newsletter servers won't accept incoming mail so your automatic replies will enter a deferred state before they finally fail to deliver.

You've proabably already know this but on the main status screen you can click on the numbers for the "In/Out Queue Size" which will give you a view of what's in the queue at that time and what state each mail is in. We normally have a number of mails in deferred state for out of office/undeliverable responses to newsletters.
Under Advanced and Queue management you'll see much the same thing but it also includes the size of the mail in bytes (the help page states kilobytes which is wrong).

The last place (I know) for checking what's happening is under Advanced and Troubleshooting. At the bottom of the page is a button for Mail Syslog which pops up a window with a live view of the mail log file.

Here's a sample entry. Entries on each line are separated by spaces. I've included a header row as best I can. I've listed question marks for the entries I don't know.;

Month date time year application process hostname/ip hostid ? ? task ENC ? MsgID Response-Code Sub-code Message
Jan 13 10:45:47 2014 barracuda outbound/smtp[17317]: 127.0.0.1 1389609941-0669804e2e87d90001-ydWOdL 0 0 SEND ENC 1 461EB3A4A0D 250 2.0.0 OK 1389609947 el2si7258800wid.74 - gsmtp

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The entries are not always the same format so the header I've listed may not always apply.
Here's a website with a decent list of response codes.
http://www.gettingemaildelivered.com/what-those-smtp-error-codes-mean-and-why-you-should-care

Something you can try is to telnet to a recipient server that is giving you problems and see that you can connect and send a few basic SMTP commands at it.
You can do this directly from the Barracuda on the Troubleshooting page (put "mailserver.domain.com 25" in the box) but you can only get the connection you can't follow up with the SMTP commands.
You can do it directly from your PC but you'll need to make sure your PC is allowed through your firewall on port 25.
An example of a SMTP Conversation over telnet would be like this (from http://www.earthinfo.org/example-smtp-conversation/);

C:\> telnet some_mailserver.net 25
SERVER SAYS: 220 some_mailserver.net ESMTP Sendmail 8.13.8/8.13.8; Thu, 23 Apr 2009 12:34:07 +0100
YOU SAY:     helo localhost.localdomain
SERVER SAYS: 250 some_mailserver..net Hello ???? [???.???.???.???] (may be forged), pleased to meet you
YOU SAY:     MAIL From:myaddress@mydomain.com
SERVER SAYS: 250 2.1.0 myaddress@mydomain.com... Sender ok
YOU SAY:     RCPT To:somone@somedomain.com
SERVER SAYS: 250 recipient <somone@somedomain.com> OK
YOU SAY:     DATA
SERVER SAYS: 354 enter mail, end with line containing only "."
YOU SAY:     Hello Fred, can you call me?
YOU SAY:     .
SERVER SAYS: 250 message sent
YOU SAY:     QUIT
SERVER SAYS: 221 goodbye

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You might also want ot see if you can implement Cacti or some other network graphing tool so that you can see you bandwidth usage on your WAN firewall port.

I have not had any emails stuck in this queue since reloading the software.