Is there anything I should watch out for with cheap "Arduino" copies?
You should rather make make a cheap Arduino by yourself. By doing this, you can have it customized and use high quality parts. You can (and should) buy the original Atmega chip so you will have 100% compatibility with the software.

You will maybe [accidentally] burn the first chip to ashes (like me), but you'll get a lot of experience doing this.

Most cheap electronics have failed me. So would cheap Arduino clone, I believe. Electronic components are kind of delicate things, capacitors and transistors especially. 

I know my answer is not real answer to the question, but you know, cheap hardware is random thing: you'll get a guys, that had luck (over 50% much likely) and those who didn't. My friend is of the second group and I'm pretty sure, he would sign under my answer.

Here, you can see a cheap way to make your own Arduino (cheaper than a pizza with Coca-Cola :)):
http://arduino.cc/en/Main/ArduinoBoardSerialSingleSided3