I contacted ConstantContact about this weeks ago. I did my own bug testing and troubleshooting that seems to point to the issue being linked with the id names that are used for the default fields. What we did as a fix was duplicate the "First Name" column on our contact list (so it appears twice) and re-import the list and map the duplicated column to a "new" custom field named "First--Name". Then when you edit your email, select insert "Contact Details" instead of the Greetings tag, and select your Custom tag instead of the default tag. This way the emails are still personalized, and the view in web browser still works.
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