What further information would allow you to make a positive identification of an organic compound from an infrared spectrum?
If you're analyzing an IR spectrum to find out what compound you have, you'll first want to look past the 1500/cm region to see what functional groups you have. For example, a 1700/cm peak will tell you you have a carbonyl, alcohols will have a peak around 3000/cm, etc. From there, pull up spectra of well known compounds with those functional groups, and compare your compound's 1500/cm to 500/cm region to them. This region is called the "fingerprint region" because it's practically unique for all molecules, so if the spectra match there, they're likely the same compound.
You can compare your IR spactra to a database entry. Usually, the database provides examples of spectra from a high purity sample and that way you can even see how pure your sample is.