You can put multiple email addresses for a given contact in gmail and you can even distinguish if it is their work or home email address. But you can't tell the difference in their profile. If you have more than one email address for a contact it will just list them without saying if it is their work or home email address even if you say what kind of email address it is.

Why is that?

Somewhat related problem in Google Docs. If a contact of yours has two email address, one johnwork.com and one johnhome.com (or something), then you can't tell from the "invited people" interface if you corrected the right one already (as you may have accidentally picked the wrong from auto-completion). They both read "john", omitting too much (the domain) for usability's sake. As a workaround, you can uninvite all John's by clicking the X, and then re-inviting the correct ones.