Playgrounds are a minefield. If you have a new walker, you won't be able to let them on their own for even five seconds, since at every turn there are things to put in their mouths/fall from and big kids barreling over your kid. Playgrounds suck. So if you can find ones that are gated and specifically for toddlers. Those are ok. But even ones that have a toddler area, all the big kids come running over to, and guess what? Your toddler only wants to play in the dangerous area. Good times.
No matter how sweet your baby is, they will grab toys out of other kids' hands and make them scream. They also may hit, bite, and push. Don't be alarmed. Every parents of a kid this age or older knows the deal; they all do it. Just correct, redirect, apologize to the other kid's parent, and move on. Eventually they will stop!
Your perfect little one-year-old eater over whom your friends and family constantly exclaim, "wow, he/she eats everything!" most likely will stop eating, sometimes entirely, and you will find your awesome adventurous Thai/Indian/Chinese child's menu reduced to bananas and milk. Again, it's ok. Just keep re-introducing foods and try not to freak out if your child has absolutely nothing for dinner. I have never once had Bumpus wake up screaming because he was hungry, even after having only eaten what felt like a thimble full of food the night before. You may find they eat a big breakfast, less for lunch, and even less for dinner. This seems fairly typical. Unless your kid is dangerously underweight, don't worry about it!
Your kid will most likely take far more pleasure in destroying your household items than playing with their arsenal of toys. This is extremely irritating. Again, they will get over it eventually!
I've found explaining things (why/where/what happens next), giving time warnings when we have to change activities, and giving basic choices (do you want a banana or apple sauce) are hugely helpful and cut down on screaming fits enormously. Might be a little advanced for a kid who just turned one, but worth a shot!
If your child starts hitting/kicking/slapping you "for fun", engaging with it (telling him no, getting mad, explaining why we don't hit) may make him think you're playing a game and will not stop the behavior. For me the only thing that stops this crap right in its tracks is saying "let's not hit, let's do hugs instead!" and giving him a huge bear hug. It sounds crazy but it works every time. My sense is sometimes kids this age get all riled up and want to physically connect with you and don't know how. So turning it into nice physicality seems to fulfill that need.
Ok, that's my been there/done that wisdom in a bottle. Hope it helps someone out there avoid some of the pitfalls I fell into!