When riding in the rain, your brakes need a bit more lead time to slow you down.......... a couple revolutions of the wheel to wipe the rain off. So always be looking and planning ahead. Give yourself a little extra space to stop.
A good idea to wipe debris off tires and off your brake pads after a rainy ride. Or it can dig into the pads and really shorten their effective life span.

Besides the painted lines, any metal grates or railroad tracks will be MUCH more slippery when wet.

Just overall - a bit more caution.

If you don't have fenders on your bike, expect to get a streak up the middle of your back. Don't wear your favorite light-colored jersey.

You'll see better if your helmet has a brim that somewhat keeps your lenses out of the direct rain.

Let's see -- that's about all I can think of for now.

annie