Loopback anomalies.
I looked but did not find any report of a problem similar to mine.
I have a new clone UNO R3. I had problems trying to install a bootloader but finally suceeded using the information from this link: http://arduino.cc/en/Tutorial/ArduinoISP The IDE (1.0.2) signalled sucessful bootloader upload. However I could not upload a sketch into the UNO. I replaced the UNO CPU with a known good one with a blink sketch loaded. UNO blinked as it should. I restored original CPU and began loopback test (using USB to UNO) with following results.
When I activated the serial monitor I was able to echo one message but incompletely, only about 40 characters, see captures 01 ~ 04. Changing the baud rate only changed the number of characters that would loopback before failure. Any attempt to send additional messages failed, yielding no looped back message. If I stopped and restarted the serial monitor I could send another message, but only one per startup of monitor. Shorter second messages disappear quickly but longer ones do not disappear until several seconds have passed.
I checked the schematic of the UNO rev3 and see that the data stream gets through the ATMEGA16U2 and as far as the 328 because there is where the jumper loops back. Because the jumper bypasses the 328 I can not see it as the problem. It works well for a while and that makes me think there is some setup jumper I am missing or maybe something to do with fuses in the 16U2 (which I know nothing about). As it stands it seems that the UNO will only allow loading via the ISP method or by using FTDI and bypassing 16U2.
The reset is jumpered to ground, the TX and RX are jumpered to each other. The angle of the photo misleads. The screen captures are from the IDE console.
The board is defective. Very likely the ATMEGA16U2 was not correctly programmed (but there could be other problems). Were I in your shoes, I would get my money back, including shipping, and buy the board somewhere (anywhere) else. To get leverage over the vendor I would make it clear they are violating the Arduino trademark and threaten to "turn them in".
If you decide to keep the board, reprogramming the ATMEGA16U2 may bring it to life.
But I am missing some skills which I will have to pick up. For example
avrdude -c usbtiny -v -p m328p
sounds great but is it a command line or makefile or what? I am not averse to learning so a pointer to a tutorial would be helpful. As stated I am using Arduino 1.0.2 and have both a Windows and Linux (Ubuntu 12.04) systems. What needs to be installed first, and where, etc. I am still getting acquainted with the Arduino stuff.