I read about this tip on Lifehacker and immediately tested it out. Sure enough, there were three or four chats that I had never noticed!
Note that the tip below can be found here: http://lifehacker.com/5576828/from-the-tips-box-ios-4-colors-portable-launchy-and-missed-ims/gallery/3
Find Missed GTalk Requests with a Gmail Search
I leave my Gmail account open in many different computers and I would venture to guess that most lifehacker readers probably do the same too. All is well except when some friend pings you on Gmail Chat and it appears only in the window that's open on the corner computer in the office. You would probably never see it and not get back to him. And that's probably not good for your friendship either.
However you can search for all such ignored pings by just searching gmail for "is:chat -me" without quotes. You'd be surprised how many rare pings you have missed in the past.
If you're the type that gets caught in this situation a lot, you could also make a bookmark using the URL for the search results page. It would give you the up-to-date results of the search every time you clicked on it. Also note that for this tip to work, you will need to have chat logging enabled in Gmail's chat settings (Settings > Chat).