Couple things...
First, lets be sure about our terminology: usually the "outbound" is the leg leaving home, taking you to your destination. The "inbound" is a little ambiguous - so I prefer the term "return" for coming home. OK, onward...
DUB is not a huge airport and is fairly easy to connect through, but it can get extremely backed up at times, if many flights have arrived around the same time. I've been in really, really long lines there to get through preclearance. You will want to be on your "A" game, getting off your first flight quickly (sit as close to the door as you can) and move swiftly through the airport to make your connection.
This bit is important: Yes, if you are on a single ticket, Aer Lingus is responsible for getting you to your destination (or home), so if your inbound flight is late and you mis-connect, you won't be stuck with a worthless ticket and a need to buy a new one (if on two separate tickets, that's a risk). But...if you misconnect, they need to put you on the next available flight. With Aer Lingus, coming back from DUB to SEA, the next available flight may be the following day. Because (unless they've added greater frequency), Aer Lingus only has a single flight from DUB to SEA per day (you might check their schedule, it varies seasonally - they may have 2 flights per day in peak summer season, less than daily in winter). So, the risk if you mis-connect is that you might get a free bonus night in Dublin. There are worse things that can happen to you, but maybe you have important stuff waiting for you and getting home one day later might throw a wrench into your plans. Note that going TO Europe, Aer Lingus has multiple flights every day (maybe not multiple flights to CDG, but they'll have more/better options). They also have partners that they MIGHT be able to rebook you on (either way) so it's not necessarily a show-stopper, but they'll have fewer options than a bigger airline like United, Lufthansa or Delta would (bigger airlines = more planes, more ways to get you home).
Non-stops from SEA to Europe are great, but often more expensive (maybe a lot more expensive than a one-stop on Aer Lingus).
Are you using Alaska miles for the flight? (just a guess...)
BTW: If you do have time to kill in DUB, check out the chocolate restaurant.