Carousel of Progress is a show that you cannot leave part way through. I think it's around 20 mins long, so keep that in mind. It can be a great place to take a nap, but if little one is cranky or needs a diaper, you can't leave. For the shows with glasses, they will likely be too big to comfortably stay on the little one's face, but they may not really care. My almost 2 yo watched it mostly without the glasses since they wouldn't stay on. Other than Carousel of Progress, you should be able to leave the other shows mid-way if needed, but try to sit at the end of a row so you aren't disturbing other guests.
Other than that, some people have said their young kids get scared of certain attractions, but it all really depends on the kid. At one, they may not really understand what's going on enough to get scared, but you know your kid best. The Buzz ride in MK and Toy Story Midway Mania in HS do whip around a bit so you'd definitely need to have a good hold on them and the little one is too young to really get into shooting the blasters, but they may still enjoy it. It's Tough to be a bug obviously shows bugs and it could frighten some little ones. Haunted Mansion and Pirates are both darker and could be scary. Many little ones don't have a problem on any of them though. I can't really think of anything without a height requirement that should just be automatically excluded for a one year old.