Well I have been Father's Day weekend a few times, last year being the most recent. The lines are long, I want to say Splash was at something like 80 minutes by the afternoon and Space Mountain was at 70 minutes by late morning. But I never wait in lines like that and you don't have to either. If you get to the park at opening or actually about 30 minutes before opening you can get so much done before the crowds build. Then you can use your fastpasses, ride the rides that are huge loaders (like POTC and Its a Small World) and of course escape over to DCA intermittently throughout the day and evening. I think Nemo will definitely increase the lines getting in the park at opening but then the rest of the park will hopefully be business as usual. Also, be aware that Sunday is an Early Entry day so if you have a park hopper with that capability or are staying onsite, by all means take advantage of that. If not, then know that on EE days, by the time the park opens up for real, Fantasyland and Tomorrowland will be mobbed already since they have been open for an hour already.
Fathers Day is always a busy weekend. Its June, So. Cal Ap's aren't totally blacked out yet and with Nemo it'll probably be somewhat insane. But I'll be there again so I guess I am not too worried!
If you want to eat at any full service restaurants, I would make those Priority Seatings as soon as you can. I have noticed places like Blue Bayou in particular fill up a bit more than usual since everyone wants to take Dad out for his special day!
