The messed up record of Andrew Hudson in the 34th Arkansas involved transcription errors. If you look closely at the service cards, you will note that a clerk later reviewed the record and noted the errors with underlines and x's. These transcription errors didn't occur often, but when they do, researchers have to do some fancy detective work; for example, the mustering officer, Capt. James B. Hensley, wasn't promoted until October 3, 1862, so he couldn't have mustered Andrew Hutson into service on January 23, 1862. Obviously, the year is 1863, and the reviewing clerk noted that fact by underlining the "2" in 1862. That's the kind of hoops you have to jump through sometimes.
Finally, the 34th Arkansas didn't disband after the fall of Little Rock. It remained in service until the end of the war, disbanding at Marshall, Texas, when the Trans-Mississippi Department was formally surrendered.
I hope this helps.