In addition to issues regarding the target modes (http://forum.square-enix.com/ffxiv/threads/1129-New-targeting-system-causing-issues), I believe one issue with targeting with a controller when using the LEFT/RIGHT buttons, is that the target marker seems to initialize based on a combination of the direction your character is facing plus what target is standing the closest (similar to what would result when simply pressing the CONFIRM button to target whatever's near you), making the targeting mechanic seem completely random and impractical.

Example: below, X is your own character, and A - F are other PCs/NPCs on the screen.
(A) (B) (C) [X] (D) (E) (F)
Let's say the camera is facing into the screen, and your actual character is physically facing the right. I want to target C, which is standing immediately to the left of my character X in relation to the camera, so pressing LEFT would seem like the obvious choice--however, since my character is physically facing right, the target marker will end up initializing on D/E/F! The target marker initializing based on the direction the character is facing makes no sense!

I used to be able to circumvent this by pressing UP/DOWN on the D-pad to target myself first, but this is no longer possible due to the new target-mode system (see post referenced above)

Suggestion: When using LEFT/RIGHT on the controller, have the target marker initialize based on the direction of the camera, or simply on your own character (this is similar to FF11 using a controller). I believe this would relieve many issues people have with the current targeting mechanic.

Controller users, can I get a "yay" on this?