Naw, for casual messing around you don't need to worry man. When I say someone might notice, I mean after like 8 hours of sustained scanning. Fot the odd scan here and there you should be fine.
The worst they can do is cut off your internet. I don't think there is anything illeagal in scanning itself. But the thing is why are you scanning other machines in the first place? I sure as hell don't think it's because you are a concerened citizen and are looking out for other people's unsecured machines. But if you find an ISP that does beleive that then let me know so I can get on there network
Either way, I wouldn't worry about. Just don't leave your puter scanning a class A subnet for a week.
As for syn packets, I'll give you a quick explanationon that.
With TCP (if you don't know what TCP is just pretend this applies to every connection your puter makes), when you connect to a remote machine the first thing that happens is the connection has to be set up by both you and the machine you are connecting to. This is done with what's called a "three way handshake". Because you are the machine that wants to make the connection, you send the other machine what's called a 'syn' packet, which is basically a request for a connection. The remote machine will respond (IF the port is open and a service is listening on the other end) with what's called a 'syn/ack' packet. This is basically an acknowledgement of your request that says "Ok, I'm listening". After you receive a syn/ack you send back an 'ack' packet to let the remote machine know you recieved it's ok, and that you are good to go. After this happens normal transmission of data can happen.
__YOUR__ ----syn---> Remote
COMPUTER <-syn/ack-- Machine
That's it in a nutshell. There is really a lot more involved than that, but this should at least give you an idea of what it is.
So.... When you send a syn packet to a port, if (and I mean IF) there is a service listening on that port then it should send a syn/ack back to you. This is how a scanner knows if a port is open or not. And just as a note, scanners do not send the ack packet back, which is why this type of scanning is sometimes called a "half open" scan, cause as you should be able to see now, it leaves the connection setup halfway through it's natural course
Ok, I'ma go eat dinner now.