How safe is an encrypted disk image?

The weak point of any encrypted file is going to be the password. Disk Utility encrypts disk images with AES encryption, which is extremely strong, so the easiest way to crack it would be to try and figure out your password. Passwords vary in strength; depending on how strong your password is, it could be very easy to very hard to crack it. Whether or not it would be worth the effort would depend entirely on the value of the encrypted data. AES encrypted data with a decent password would probably not be worth attempting to decrypt unless it contained nuclear secrets or the like.

The same goes for deleted files. Overwriting the data once would probably be enough to defeat most recovery utilities. The more times you overwrite the data, the more difficult and more expensive it becomes to recover. I've heard of files overwritten more than 7 times being almost entirely recovered, but only at great effort and expense. Whether or not the effort and expense was worth it would depend on the value of the deleted data.

My company produces one of the premier encryption cracking programs used by law enforcement in the US, and there are certainly some files that would take a great deal of computer time and effort to crack, depending on the encryption algorithm and quality of the password.

See this article for information about the security used by encrypted disk images, and here for data recovery.

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