Turns out, it is a problem with "AT&T Messages" which is a replacement for the messaging app that came with the phone. I've done some more in-depth analysis as to what and where the problem happens.
Here's what happens. When I press the letter "I", the pop-up letter beneath my finger shows the letter "I", the message box shows the letter "I", but the predictive text bar shows the first choice of "U". The letter "U" is highlighted in blue. If I press the space bar, the letter "U" is now in the message box. The keyboard shows me typing the letter "I", but the predictive text things what I really meant to type is one letter to the left.
The same thing happens with the letters O, P, J, K, L, B, N, and M. I press the letter, the correct letter shows up in the message box, but the predictive text shows the letter to the left of what I type, and THAT letter is highlighted. All other letters work correctly.
This only happens in landscape mode in the AT&T Messages app.
When I type "I love you" to my wife, what I see, when I'm done typing CORRECTLY is "U live you".
When I type the word "ironic", the screen is showing this nonsensical crap: "urinuc". Granted, the word "ironic" is highlighted on the predictive text bar, but it is the second selection.
I've posted a message to the AT&T support forums, but no response as of yet. I like just about everything else about the AT&T Messages app. For now, I'm texting in portrait format.