Creating separate bug / feature cases from Inbox cases is definitely the best way to make sure that every issue gets attention and every customer email gets a prompt response. You can keep the Inbox cases in your support department's filters and make sure that bugs and features go to developers while maintaining the link between them.
I use a bookmarklet created by Rich Armstrong's yet-to-be-released magical FogBugz bookmarklet generator. This answer is one to clone a case. Here's what I use to create a related case. You can tweak the text, and when you use it, it will put any text you highlight before you hit it into the body of the new case. Line breaks have been added here for readability. The whole thing should be on one line.
javascript:a=function%20(){%20open('http://**[your fogbugz url]**/default.asp?
command=new&pg=pgEditBug&ixCategory=1&ixProject=[desired project]&ixArea=
[desired area]&ixPersonAssignedTo='+goBug.ixPersonAssignedTo+'
&sCustomerEmail='%20+%20escape(goBug.sCustomerEmail)%20+%20'
&ixPriority='+goBug.ixPriority+'&sTitle='%20+%20escape(goBug.sTitle)%20+%20'
&sTags='%20+%20escape(goBug.ListTagsAsArray())%20+%20'
&sEvent=See%20Case%20'%20+%20goBug.ixBug%20+%20escape('\r\n\r\n')%20+%20%20
escape(document.getSelection())%20+%20'&b=c');%20return;};a();
This one makes a see-also relation and copies the correspondent, title, tags, etc. You could play with it and make it be a subcase or a parent case. If you need help with that, let us know.