I have a song that has an annoying minute long silence at the end. Can I get rid of it?

Yes. Well not get rid of it, but you can fool iTunes into skipping over the silence and onto the next song. While playing the track in iTunes make a note of the point you want the song to end by watching the Elapsed Time progress bar.

Press the Command-i which will open the song info window. Select the options tab and select enable stop time, then edit the time to the point you wish the track to finish. Click OK.

When you next play the track, iTunes will stop at the new time. Although the whole track will be copied to your iPod it is smart enough to end the track at the time point you have selected.