You may be looking for a service like http://getsatisfaction.com/ or http://uservoice.com/ . They are very customer oriented, and I saw how they were used both for software products and for feedback on other issues.
In addition, I got Mantis to receive email directly with both new and existing problems - f.ex. if the subject contains a problem number, such as [1234], the email becomes a 1234 release note.
Thus, the client does not know about Mantis, you can pay for Mantis with release numbers, and you can customize the workflow in Mantis very much in accordance with your process needs.
In addition, you may have separate projects in Mantis that can receive from different email addresses, for example, one for errors and one for support.
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