Question: I would like to know to know why UART errors occur, and when one should check for such errors. There is a post on here that asks about handling individual errors, such as overrun, parity, etc... I am clear on why data overrun happens, why parity error happens, but I would like to know what is the root cause. My question is more focused on why these errors could occur (physical reasons), and when one should do make error checking a factor for their application.

So far my program seems to work great (with no error checking), but I know that noise can mess things up. How could I simulate conditions that could cause the UART Rx/Tx ports to fail?

Answer: 
One common source of errors on UART besides signal level quality (noise, rise/fall times) is clock skew. If the transmitter clock and receiver clock are not derived from the same source (which is the case most of the time), then one will run faster than the other. When the timing error is too large, you may occasionally read a wrong bit.
In order to deal with these errors, you must implement a higher level logical protocol. something akin to TCP, or check the OSI stack for ideas. 

basically, two important parts to start with are checksums, and timeouts. use an algorithm to compute a redundent value that represents, in a smaller form, the contents of each message. then check this in the received message. if the sums don't match, you have possibly gotten a framing error, bit noise, etc, etc. and you'll need to discard the message and attempt some sort of recovery, resend, NACK ( not acknlowledged )signal, etc.

also, make sure to implement timeouts in your upper level protocol. if you get some kind of framing error, your UART may never recover and begin processing again. it may be waiting for the stop bit on a frame that the sender UART thinks has already been sent, but was corrupted by noise , clock skew, etc. this will send any input code into an infinite loop. make sure that you have a sane limit as to how long your input reading should wait until deciding to abandon this message, and again, retry, NACK, abandon, etc.