One of the non-obvious things that's a good idea for that hike is a pair of old sneakers (or perhaps some waterproof running sandals) that you can wear while wading in the river.

Once you get to the river, you need to wade to move up and down the canyon. Switch out of your hiking boots and put your river shoes on. Moving from camp to the springs and back usually requires wading, and it's much faster if your feet are protected while under water. Expect to spend your time there wearing wet river shoes, and keep your boots dry for the trip out.

I've seen the river be fairly high in early season. If it's too high to cross safely, you probably ought to bail on the springs and backtrack to the previous camping spot, the one that's about 2/3 the way in.

The middle fork of the Big Sur River is a good place to make sure that you do not get hurt. When I tripped and sliced open my finger, I had to walk all the way out the next day, only to find that Big Sur has no Emergency Medical Services. The closest EMS were in Monterey, and by then it was better to keep on driving until I got home. If someone were to hurt their legs or feet, they could pay hell to get out of the back country. I have heard reports of Mountain Rescue having to float people out via the river in body bags. Make it a point to not take any unneccessary chances.

I've seen scorpions and snakes in that area. The biggest pests are the birds (because they will steal your food), but the horseflies can be obnoxious at some parts of the season (fortunately, the horseflies stop bothering you around sundown). I've had good times with strangers there, but I've also encountered obnoxious idiots.

I've never gone down-river to get back out, but I've been told that it's a BAD idea. At one or more points you have to swim, and that's not a great thing to do while you are trying to keep your pack dry.

I hope you have a good trip!