My flat iron's (for clothes) plug fell in a bucket of water. I pulled it out almost immediately.
If I let it dry, is there any concern if I use it or is it not safe anymore?
Take the cover off and inspect, if all dry and clean without corrosion then good to go.
If it is a "new" molded plug, then dry with a tissue and should be good. If worried wait 24h. However, with either position above, test for continuity between both pins and the earth or ground connection. If a low resistance is measured then either water is still causing a short or something else may be wrong. Checking for continuity between the pins may just be measuring the normal resistance of the device.
What's really bad is electricity plus water:
That causes electrolysis, and that will eat through the metal contacts very quickly.
There's a risk for the user if the wet parts are touched.
As long as you don't plug it in while wet, and let it dry, it'll be fine.
You can leave the device in a hot environment to dry it, for example in a car parked in the sun for a few days.
I'd change the plug just to be safe.
You don't know what the inside of the plug looks like - nor can you open it to see. You don't know what little nooks & crannies could hold water for several days before it dries fully, so a 24h wait might or might not be long enough - you'll find out when you plug it in… if it goes bang you didn't wait long enough.
After that, there's corrosion. Wires tend to be copper. Plug innards tend to be brass, which contains copper. Copper will verdigris [oxidise] after some time in a wet environment which in extreme circumstances can completely 'rot' away the copper. That may never become an issue depending on how the wires are connected to the plug pins… but again as it's a moulded plug, you'll never be able to see for sure.
So, for the sake of a buck & 5 minutes of your time - change the plug.