When purchasing a used Acoustic guitar you should be sure to check that the following are all in fine condition before purchasing.

Body
Be sure the body is not damaged in anyway. The body of a acoustic guitar is one of the most important parts of a guitar. The body gives out the sound projection and tonal accent. A damaged body will have severe effects on the tone.
Neck
You must ensure that the neck of the acoustic guitar is not warped or damaged. The nick of an acoustic guitar is mainly used to determine how many frets.
Intonation
This is a key element to check for when purchasing a used acoustic guitar. The intonation will decided if the guitar can notes play in tune as you shift up the neck.
Bridge and Fingerboard
Although the condition of the bridge and fingerboard to not have a severe impact on the quality or tonal sounds of the acoustic guitar, you should still check to be sure it is intact and in good condition.
Finish
Although the finish does not have an impact on the sound quality of your guitar, scratches, dents, damage could show lack of care taken for the guitar.