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
You could be buying counterfeit products, with counterfeit chips or components. It sounds unbelievable, but check out Sparkfun's research on counterfeit ATMega328 (the same chip in many Arduino boards, clones, and variants!)
This article starts here (why aren't these ATmegas acting correctly?):
https://www.sparkfun.com/news/350
Second page: (they're not ATmegas at all):
https://www.sparkfun.com/news/395
There are so many known good variants out there. Pick one that people have actually heard of instead of something sketchy.
- EMSL's Diavolino http://shop.evilmadscientist.com/productsmenu/tinykitlist/180-diavolino
- Modern Device http://shop.moderndevice.com/collections/arduino-freeduino/
- Digispark http://digistump.com/category/1
Even though I prefer that you make your Arduino rather buying it, if you're interested in buying cheap copies it's not an issue. I bought a Mega for as low as 16$ and a Nano for like 10$ since I started with electronics, they are working completely fine and a good acceptable quality.
Just beware of 1 thing, some of them come with Prolific drivers for USB to serial, you'll have problem finding working drivers for your OS. Make sure it is FTDI and not Prolific, the drivers will be included with the Arduino IDE.