If you already have a seat assignment I would check in at 7.00am - Checking in 2 hours prior to flight deparure at Shannon gives you plenty of time to get through security and immigration.
If you have a seat assignment already or can check in online, choose your seat and print your own boarding card then I'd say you'd be mad to turn up 3 hrs before your flight (especially when that means being there at 6am) ...
I'm not a regular at Shannon, but I don't imagine the security queues are too bad at all, and there's not that much to do for 2hrs and 58mins after you get through security - I'd arrive 2 hours before max, personally I'd probably do 90 minutes - but each to their own
Edited to add - You can't yet checkin online for Continental flights departing from DUB or SNN (Wonder why - you can check in for anwhere apart from Ireland, Switzerland and the Cayman Islands on Continental.com !) ... which is a bit of a pain - but still I wouldn't turn up 3hrs before (especially if you've got your seats already assigned - if you haven't done this already you should call Continental and ask for this)